//---------------------------------------------------------------------
// CascadeSharp
// General Public License V2
//---------------------------------------------------------------------

using System;

namespace CascadeSharp.TKMath.math
{
    //---------------------------------------------------------------------
    //  Class  math
    //---------------------------------------------------------------------
    public sealed class math
    {
        /// <summary>
        /// // The GPoints method return a vector of Gaussian points.
        /// The following calculation makes it possible to have stored only
        /// half of the points given that they are repeated twice.
        /// </summary>
        /// <param name="Index"></param>
        /// <param name="GPoint"></param>
        public static void GaussPoints(int Index, out Vector GPoint)
        {
            //The C++ implementation would ask for a 11 elements array and return
            // the first element as zero, this looks incorrect so I'm fixing it
            //or maybe I'm too dumb to understand the math behind it
            int Som = 0;
            int i;
            int ind = (Index + 1) >> 1;
            GPoint = new Vector(Index);
            GPoint.Init(0);

            for (i = 1; i < Index; i++)
            {
                Som += (i + 1) >> 1;
            }
            
            for (i = 1; i <= ind; i++)
            {
                GPoint[i-1] = GaussPoint[Som + i];
                GPoint[i + ind-1] = -GPoint[i-1];
            }
        }

        /// <summary>
        /// // The GWeights method return a vectos of Gaussian weights.
        /// The following calculation makes it possible to have stored only
        /// half of the points given that they are repeated twice.
        /// </summary>
        /// <param name="Index"></param>
        /// <param name="GWeight"></param>
        public static void GaussWeights(int Index, out Vector GWeight)
        {
            //The C++ implementation would ask for a 11 elements array and return
            // the first element as zero, this looks incorrect so I'm fixing it
            //or maybe I'm too dumb to understand the math behind it
            int Som = 0;
            int i;
            int ind = (Index + 1) >> 1;
            GWeight = new Vector(Index);
            GWeight.Init(0);

            for (i = 1; i < Index; i++)
            {
                Som += (i + 1) >> 1;
            }
            
            for (i = 1; i <= ind; i++)
            {
                GWeight[i-1]= GaussWeight[Som + i];
                GWeight[i + ind-1] = GWeight[i-i];
            }
        }

        /// <summary>
        /// Returns a vector of Gauss points and a vector of their weights.
        /// The difference with the
        /// method GaussPoints is the following:
        /// - the points are returned in increasing order.
        /// - if Index is greater then GaussPointsMax, the points are
        /// computed.
        /// Returns Standard_True if Index is positive, Points' and Weights'
        /// length is equal to Index, Points and Weights are successfully computed.
        /// </summary>
        /// <param name="Index"></param>
        /// <param name="Points"></param>
        /// <param name="Weights"></param>
        /// <returns></returns>
        public static bool OrderedGaussPointsAndWeights(int Index, out Vector Points, out Vector Weights)
        {
            if (Index < 1)
            {
                Points = null;
                Weights = null;
                return false;
            }

            Points = new Vector(Index);
            Points.Init(0);
            Weights = new Vector(Index);
            Weights.Init(0);
            
            if (Index <= 61)
            {
                // Get points from the array.
                int i;
                int aStartInd = 1;

                // Compute the index of starting point in the array.
                for (i = 1; i < Index; i++)
                    aStartInd += (i + 1) / 2;

                // Get points from the array.
                int aNbPts = Index / 2;
                int aLowerI = Points.Lower();
                int anUpperI = Points.Upper();

                for (i = 0; i < aNbPts; i++)
                {
                    Points[aLowerI + i]= -GaussPoint[aStartInd + i];  
                    Points[anUpperI - i]= GaussPoint[aStartInd + i]; 
                    Weights[aLowerI + i]= GaussWeight[aStartInd + i];
                    Weights[anUpperI - i]= GaussWeight[aStartInd + i];
                }

                if (Index % 2 == 1)
                {
                    // Index is odd.
                    Points[aLowerI + i] = GaussPoint[aStartInd + i];
                    Weights[aLowerI + i] = GaussWeight[aStartInd + i];
                }

                return true;
            }
            else
            {
                var PWcomputer = new math_ComputeGaussPointsAndWeights(Index);
                if (!PWcomputer.IsDone())
                    return false;
                Points = PWcomputer.Points();
                Weights = PWcomputer.Weights();
                return true;
            }
        }
        /// <summary>
        /// Returns a vector of Kronrod points and a vector of their
        /// weights for Gauss-Kronrod computation method.
        /// Index should be odd and greater then or equal to 3,
        /// as the number of Kronrod points is equal to 2*N + 1,
        /// where N is a number of Gauss points. Points and Weights should
        /// have the size equal to Index. Each even element of Points
        /// represents a Gauss point value of N-th Gauss quadrature.
        /// The values from Index equal to 3 to 123 are stored in a
        /// table (see the file math_Kronrod.cxx). If Index is greater,
        /// then points and weights will be computed. Returns Standard_True
        /// if Index is odd, it is equal to the size of Points and Weights
        /// and the computation of Points and Weights is performed successfully.
        /// Otherwise this method returns Standard_False.
        /// </summary>
        /// <param name="Index"></param>
        /// <param name="Points"></param>
        /// <param name="Weights"></param>
        /// <returns></returns>
        public static bool KronrodPointsAndWeights(int Index, ref Vector Points, ref Vector Weights)
        {
            if (Index < 3 ||   // Index is less then 3
                Index % 2 == 0 ||   // Index is even
                Points.Length() != Index || // Inconsistent length of Points
                Weights.Length() != Index)   // Inconsistent length of Weights
                return false;

            if (Index <= 123)
            {
                // Get points from the array.
                int i;
                int aStartInd = 0;

                // Compute the index of starting point in the array.
                for (i = 3; i < Index; i += 2)
                    aStartInd += (i + 1) / 2;

                // Get points from the array.
                int aNbPts = i / 2;
                int aLowerI = Points.Lower();
                int anUpperI = Points.Upper();

                for (i = 0; i < aNbPts; i++)
                {
                    Points.SetValue(aLowerI + i, -KronrodPoint[aStartInd + i]);
                    Points.SetValue(anUpperI - i, KronrodPoint[aStartInd + i]);
                    Weights.SetValue(aLowerI + i, KronrodWeight[aStartInd + i]);
                    Weights.SetValue(anUpperI - i, KronrodWeight[aStartInd + i]);
                }
                Points.SetValue(aLowerI + aNbPts, KronrodPoint[aStartInd + aNbPts]);
                Weights.SetValue(aLowerI + aNbPts, KronrodWeight[aStartInd + aNbPts]);

                return true;
            }
            else
            {
                var PWcomputer = new math_ComputeKronrodPointsAndWeights((Index-1)/ 2);
                if (!PWcomputer.IsDone())
                    return false;
                Points = PWcomputer.Points();
                Weights = PWcomputer.Weights();
                return true;
            }
        }

        #region Constants
        /// <summary>
        /// Returns the maximal number of points for that the values
        /// are stored in the table. If the number is greater then
        /// GaussPointsMax, the points will be computed.
        /// </summary>
        public const int GaussPointsMax = 61;

        /// <summary>
        /// Returns the maximal number of points for that the values
        /// are stored in the table. If the number is greater then
        /// KronrodPointsMax, the points will be computed.
        /// </summary>
        public const int KronrodPointsMax = 123;

        public static readonly double[] GaussPoint =
        {
            0.0e+00,
            0.0e+00, // N = 1
            0.577350269189625764509148780501958e+00, // N = 2
            0.774596669241483377035853079956480e+00, // N = 3
            0.0e+00,
            0.861136311594052575223946488892810e+00, // N = 4
            0.339981043584856264802665759103245e+00,
            0.906179845938663992797626878299393e+00, // N = 5
            0.538469310105683091036314420700209e+00,
            0.0e+00,
            0.932469514203152027812301554493994e+00, // N = 6
            0.661209386466264513661399595019906e+00,
            0.238619186083196908630501721680712e+00,
            0.949107912342758524526189684047851e+00, // N = 7
            0.741531185599394439863864773280789e+00,
            0.405845151377397166906606412076961e+00,
            0.0e+00,
            0.960289856497536231683560868569472e+00, // N = 8
            0.796666477413626739591553936475831e+00,
            0.525532409916328985817739049189246e+00,
            0.183434642495649804939476142360184e+00,
            0.968160239507626089835576202903672e+00, // N = 9
            0.836031107326635794299429788069735e+00,
            0.613371432700590397308702039341474e+00,
            0.324253423403808929038538014643337e+00,
            0.0e+00,
            0.973906528517171720077964012084452e+00, // N = 10
            0.865063366688984510732096688423493e+00,
            0.679409568299024406234327365114874e+00,
            0.433395394129247190799265943165784e+00,
            0.148874338981631210884826001129720e+00,
            0.978228658146056992803938001122856e+00, // N = 11
            0.887062599768095299075157769303928e+00,
            0.730152005574049324093416252031154e+00,
            0.519096129206811815925725669458610e+00,
            0.269543155952344972331531985400861e+00,
            0.0e+00,
            0.981560634246719250690549090149283e+00, // N = 12
            0.904117256370474856678465866119096e+00,
            0.769902674194304687036893833212819e+00,
            0.587317954286617447296702418940535e+00,
            0.367831498998180193752691536643721e+00,
            0.125233408511468915472441369463853e+00,
            0.984183054718588149472829448807119e+00, // N = 13
            0.917598399222977965206547836500699e+00,
            0.801578090733309912794206489582858e+00,
            0.642349339440340220643984606995517e+00,
            0.448492751036446852877912852127640e+00,
            0.230458315955134794065528121097989e+00,
            0.0e+00,
            0.986283808696812338841597266704064e+00, // N = 14
            0.928434883663573517336391139377848e+00,
            0.827201315069764993189794742650405e+00,
            0.687292904811685470148019803019327e+00,
            0.515248636358154091965290718551190e+00,
            0.319112368927889760435671824168475e+00,
            0.108054948707343662066244650219835e+00,
            0.987992518020485428489565718586659e+00, // N = 15
            0.937273392400705904307758947710112e+00,
            0.848206583410427216200648320774263e+00,
            0.724417731360170047416186054613928e+00,
            0.570972172608538847537226737253913e+00,
            0.394151347077563369897207370981046e+00,
            0.201194093997434522300628303394596e+00,
            0.0e+00,
            0.989400934991649932596154173450404e+00, // N = 16
            0.944575023073232576077988415534452e+00,
            0.865631202387831743880467897712467e+00,
            0.755404408355003033895101194847403e+00,
            0.617876244402643748446671764048800e+00,
            0.458016777657227386342419442983577e+00,
            0.281603550779258913230460501460496e+00,
            0.950125098376374401853193354249581e-01,
            0.990575475314417335675434019940707e+00, // N = 17
            0.950675521768767761222716957895783e+00,
            0.880239153726985902122955694488141e+00,
            0.781514003896801406925230055520479e+00,
            0.657671159216690765850302216643003e+00,
            0.512690537086476967886246568629553e+00,
            0.351231763453876315297185517095346e+00,
            0.178484181495847855850677493654066e+00,
            0.0e+00,
            0.991565168420930946730016004706406e+00, // N = 18
            0.955823949571397755181195892928630e+00,
            0.892602466497555739206060591127977e+00,
            0.803704958972523115682417455014383e+00,
            0.691687043060353207874891081288922e+00,
            0.559770831073947534607871548525322e+00,
            0.411751161462842646035931793833052e+00,
            0.251886225691505509588972854877911e+00,
            0.847750130417353012422618529357838e-01,
            0.992406843843584403189017670254354e+00, // N = 19
            0.960208152134830030852778840685415e+00,
            0.903155903614817901642660928533756e+00,
            0.822714656537142824978922486712007e+00,
            0.720966177335229378617095860824125e+00,
            0.600545304661681023469638164946193e+00,
            0.464570741375960945717267148104109e+00,
            0.316564099963629831990117328849845e+00,
            0.160358645640225375868096115740744e+00,
            0.0e+00,
            0.993128599185094924786122388473126e+00, // N = 20
            0.963971927277913791267666131192107e+00,
            0.912234428251325905867752441208091e+00,
            0.839116971822218823394529061698667e+00,
            0.746331906460150792614305070356382e+00,
            0.636053680726515025452836696226146e+00,
            0.510867001950827098004364050955266e+00,
            0.373706088715419560672548177024927e+00,
            0.227785851141645078080496195368575e+00,
            0.765265211334973337546404093988382e-01,
            0.993752170620389500260242035940332e+00, // N = 21
            0.967226838566306294316622214904022e+00,
            0.920099334150400828790187133718838e+00,
            0.853363364583317283647250638585182e+00,
            0.768439963475677908615877851306936e+00,
            0.667138804197412319305966669990138e+00,
            0.551618835887219807059018796724313e+00,
            0.424342120207438783573668888543788e+00,
            0.288021316802401096600792516064600e+00,
            0.145561854160895090937030982338686e+00,
            0.0e+00,
            0.994294585482399292073031421168066e+00, // N = 22
            0.970060497835428727123950986748560e+00,
            0.926956772187174000520692939267243e+00,
            0.865812577720300136536425637014974e+00,
            0.787816805979208162004277955410719e+00,
            0.694487263186682780050689835761995e+00,
            0.587640403506911592958876927638605e+00,
            0.469355837986757026406330710966410e+00,
            0.341935820892084225158147420427379e+00,
            0.207860426688221285478846533919546e+00,
            0.697392733197222212138417961186281e-01,
            0.994769334997552123523925715452405e+00, // N = 23
            0.972542471218115231956024076799993e+00,
            0.932971086826016102349196989085222e+00,
            0.876752358270441667378156885913797e+00,
            0.804888401618839892151118407002211e+00,
            0.718661363131950194461624483747842e+00,
            0.619609875763646156385097311649803e+00,
            0.509501477846007549689793047866828e+00,
            0.390301038030290831421488872880605e+00,
            0.264135680970344930533869538283309e+00,
            0.133256824298466110931742682241766e+00,
            0.0e+00,
            0.995187219997021360179997409695963e+00, // N = 24
            0.974728555971309498198391993040647e+00,
            0.938274552002732758523649001703114e+00,
            0.886415527004401034213154341985133e+00,
            0.820001985973902921953949872662897e+00,
            0.740124191578554364243828103101925e+00,
            0.648093651936975569252495786909868e+00,
            0.545421471388839535658375617218405e+00,
            0.433793507626045138487084231913343e+00,
            0.315042679696163374386793291319810e+00,
            0.191118867473616309158639820757070e+00,
            0.640568928626056260850430826247450e-01,
            0.995556969790498097908784946893469e+00, // N = 25
            0.976663921459517511498315386374828e+00,
            0.942974571228974339414011169665041e+00,
            0.894991997878275368851042006816693e+00,
            0.833442628760834001421021108670646e+00,
            0.759259263037357630577282865216328e+00,
            0.673566368473468364485120633243234e+00,
            0.577662930241222967723689841613256e+00,
            0.473002731445714960522182115009143e+00,
            0.361172305809387837735821730127642e+00,
            0.243866883720988432045190362797452e+00,
            0.122864692610710396387359818808037e+00,
            0.0e+00,
            0.995885701145616929003216959418519e+00, // N = 26
            0.978385445956470991100580354051874e+00,
            0.947159066661714250135915283481245e+00,
            0.902637861984307074217665599020455e+00,
            0.845445942788498018797507061452577e+00,
            0.776385948820678856192967247265337e+00,
            0.696427260419957264863813913722192e+00,
            0.606692293017618063231978746918554e+00,
            0.508440714824505717695703064725394e+00,
            0.403051755123486306481077377098892e+00,
            0.292004839485956895142835382077830e+00,
            0.176858820356890183969057748418345e+00,
            0.592300934293132070937185751984034e-01,
            0.996179262888988566938887208663978e+00, // N = 27
            0.979923475961501222855873354920358e+00,
            0.950900557814705006851908031700108e+00,
            0.909482320677491104300645017620528e+00,
            0.856207908018294490302737222871666e+00,
            0.791771639070508227144397344046227e+00,
            0.717013473739423699294816211647746e+00,
            0.632907971946495140927734637635987e+00,
            0.540551564579456894900300941559567e+00,
            0.441148251750026880585974155689329e+00,
            0.335993903638508899730319034207283e+00,
            0.226459365439536858857239107360230e+00,
            0.113972585609529966932894983869977e+00,
            0.0e+00,
            0.996442497573954449950436390674007e+00, // N = 28
            0.981303165370872753694559944854359e+00,
            0.954259280628938197254101840656842e+00,
            0.915633026392132073869689422403264e+00,
            0.865892522574395048942254567705472e+00,
            0.805641370917179171447885955315246e+00,
            0.735610878013631772028144510330697e+00,
            0.656651094038864961219898176506815e+00,
            0.569720471811401719308003283356526e+00,
            0.475874224955118261034411847667546e+00,
            0.376251516089078710221357209556062e+00,
            0.272061627635178077676826356125771e+00,
            0.164569282133380771281471777891166e+00,
            0.550792898840342704265165273418800e-01,
            0.996679442260596586163191533987124e+00, // N = 29
            0.982545505261413174870926010927766e+00,
            0.957285595778087725798208042852482e+00,
            0.921180232953058785093753432653503e+00,
            0.874637804920102790417793422545473e+00,
            0.818185487615252444989572213975722e+00,
            0.752462851734477133912610077390281e+00,
            0.678214537602686515156185005352085e+00,
            0.596281797138227820379586211191379e+00,
            0.507592955124227642102627919627335e+00,
            0.413152888174008663890706586031623e+00,
            0.314031637867639934948195923191050e+00,
            0.211352286166001074506375728902937e+00,
            0.106278230132679230170982392430377e+00,
            0.0e+00,
            0.996893484074649540271630055317671e+00, // N = 30
            0.983668123279747209970032570528774e+00,
            0.960021864968307512216871038176021e+00,
            0.926200047429274325879324263685316e+00,
            0.882560535792052681543116468889778e+00,
            0.829565762382768397442898117701654e+00,
            0.767777432104826194917977341463632e+00,
            0.697850494793315796932292387934439e+00,
            0.620526182989242861140477556432087e+00,
            0.536624148142019899264169793311055e+00,
            0.447033769538089176780609900322852e+00,
            0.352704725530878113471037207089371e+00,
            0.254636926167889846439805129817806e+00,
            0.153869913608583546963794672743256e+00,
            0.514718425553176958330252131667226e-01,
            0.997087481819477074055626559184650e+00, // N = 31
            0.984685909665152484002465158219724e+00,
            0.962503925092949661789052419632531e+00,
            0.930756997896648164956945747416761e+00,
            0.889760029948271043374192015019185e+00,
            0.839920320146267340086904533281437e+00,
            0.781733148416624940406360021026438e+00,
            0.715776784586853283905970865155319e+00,
            0.642706722924260346184418203261165e+00,
            0.563249161407149262720944923592216e+00,
            0.478193782044902480440594039356646e+00,
            0.388385901608232943061351461287458e+00,
            0.294718069981701616617903897671709e+00,
            0.198121199335570628772412996032834e+00,
            0.995553121523415203251747901189407e-01,
            0.0e+00,
            0.997263861849481563544981151066702e+00, // N = 32
            0.985611511545268335400174989274245e+00,
            0.964762255587506430773812000051285e+00,
            0.934906075937739689170919084567802e+00,
            0.896321155766052123965307272525312e+00,
            0.849367613732569970133692995170930e+00,
            0.794483795967942406963097301414607e+00,
            0.732182118740289680387426664868980e+00,
            0.663044266930215200975115168614811e+00,
            0.587715757240762329040745476415515e+00,
            0.506899908932229390023747474377153e+00,
            0.421351276130635345364119436172526e+00,
            0.331868602282127649779916805730176e+00,
            0.239287362252137074544603209165502e+00,
            0.144471961582796493485186373598811e+00,
            0.483076656877383162348125704405022e-01,
            0.997424694246455217266168057363019e+00, // N = 33
            0.986455726230642488110375576002027e+00,
            0.966822909689992768928377784220078e+00,
            0.938694372611168350355835047808460e+00,
            0.902316767743433583040531371887830e+00,
            0.858009652676504064643061459435014e+00,
            0.806162356274166589796200875764785e+00,
            0.747230496449562157859055125262398e+00,
            0.681731959969742786268215946711838e+00,
            0.610242345836379027307287513572929e+00,
            0.533389904786347643548894264990158e+00,
            0.451850017272450695725993277240885e+00,
            0.366339257748073341070220623253855e+00,
            0.277609097152497029403248067298325e+00,
            0.186439298827991572335798759218823e+00,
            0.936310658547333856707429241225377e-01,
            0.0e+00,
            0.997571753790841919243372472354684e+00, // N = 34
            0.987227816406309485049750276055879e+00,
            0.968708262533344281764646612095310e+00,
            0.942162397405107091631675938590244e+00,
            0.907809677718324468800899846638584e+00,
            0.865934638334564469263572125352058e+00,
            0.816884227900933664591578886354187e+00,
            0.761064876629873014187408974381904e+00,
            0.698939113216262907933000105154353e+00,
            0.631021727080528545317775755554132e+00,
            0.557875500669746642736459886196742e+00,
            0.480106545190327034194102680508252e+00,
            0.398359277758645940631494752932366e+00,
            0.313311081339463247458316765650981e+00,
            0.225666691616449483868641180934347e+00,
            0.136152357259182975894428824331118e+00,
            0.455098219531025427490756708519302e-01,
            0.997706569099600297260163068601969e+00, // N = 35
            0.987935764443851498035117246119705e+00,
            0.970437616039229833215070385421235e+00,
            0.945345148207827329538726062559940e+00,
            0.912854261359317614464936993689573e+00,
            0.873219125025222331523282385917057e+00,
            0.826749899092225406834050580360608e+00,
            0.773810252286912555267423021824143e+00,
            0.714814501556628783264408628981906e+00,
            0.650224364665890388675792808879740e+00,
            0.580545344749764509934502008212914e+00,
            0.506322773241488615024297555830838e+00,
            0.428137541517814254187620613002552e+00,
            0.346601554430813945876979834930152e+00,
            0.262352941209296057970895200455586e+00,
            0.176051061165989569974303656445059e+00,
            0.883713432756592636009294334975488e-01,
            0.0e+00,
            0.997830462484085836198828499668270e+00, // N = 36
            0.988586478902212238073394890424680e+00,
            0.972027691049697949335606399404572e+00,
            0.948272984399507545202473277937562e+00,
            0.917497774515659066075868287255494e+00,
            0.879929800890397131982427042693919e+00,
            0.835847166992475306418820992281084e+00,
            0.785576230132206512827768932425190e+00,
            0.729489171593556582090260484147818e+00,
            0.668001236585521062097191342519143e+00,
            0.601567658135980535079944975520867e+00,
            0.530680285926245161640709080064297e+00,
            0.455863944433420267207217669332683e+00,
            0.377672547119689216322736389669641e+00,
            0.296684995344028270503239047745163e+00,
            0.213500892316865578943226228902714e+00,
            0.128736103809384788651993388005152e+00,
            0.430181984737086072269689782283634e-01,
            0.997944582477913648940802962682757e+00, // N = 37
            0.989185963214319186684100640799317e+00,
            0.973493030056485744328890223257303e+00,
            0.950972343262094821328576499759667e+00,
            0.921781437412463742668143131089868e+00,
            0.886124962155486078946149640462293e+00,
            0.844252987340555967987456380756328e+00,
            0.796459200509902293393046321552176e+00,
            0.743078833981965262547047434759654e+00,
            0.684486309130959357445523205836641e+00,
            0.621092608408924483148152592597942e+00,
            0.553342391861581781235098358083604e+00,
            0.481710877803205554147192868895960e+00,
            0.406700509318326110100931591612872e+00,
            0.328837429883706999498471801339985e+00,
            0.248667792791365758805567751487718e+00,
            0.166753930239851976968671730411824e+00,
            0.836704089547699019430483317363992e-01,
            0.0e+00,
            0.998049930535687619812846987992053e+00, // N = 38
            0.989739454266385571944427184549425e+00,
            0.974846328590153507640884569979646e+00,
            0.953466330933529595670542153154359e+00,
            0.925741332048584396825110560639529e+00,
            0.891855739004632216794935748571609e+00,
            0.852035021932362188859650175764213e+00,
            0.806544167605316815551565212410440e+00,
            0.755685903753970680737738187149712e+00,
            0.699798680379184355912825816848099e+00,
            0.639254415829681707180344873289419e+00,
            0.574456021047807081132927500483698e+00,
            0.505834717927931103240533716513971e+00,
            0.433847169432376484373256162517984e+00,
            0.358972440479435013256717621456562e+00,
            0.281708809790165261360114071418698e+00,
            0.202570453892116703203977781514606e+00,
            0.122084025337867419869612381329407e+00,
            0.407851479045782399133164323297849e-01,
            0.998147383066432906005467835672606e+00, // N = 39
            0.990251536854685983639785745206178e+00,
            0.976098709333471053844837496021669e+00,
            0.955775212324652277110903358756271e+00,
            0.929409148486738229697812287670748e+00,
            0.897167119292992887848293304361943e+00,
            0.859252937999906153913796656392845e+00,
            0.815906297430143104353232829495897e+00,
            0.767401242931063499832272373900357e+00,
            0.714044435894534679133867003267531e+00,
            0.656173213432010910734425938336971e+00,
            0.594153454957277988692890073931302e+00,
            0.528377268660437473896343635816299e+00,
            0.459260512309136048663246633114183e+00,
            0.387240163971561455853881965636262e+00,
            0.312771559248185922535996911785674e+00,
            0.236325512461835767336006327332651e+00,
            0.158385339997837799922701061361399e+00,
            0.794438046087554775819170831926406e-01,
            0.0e+00,
            0.998237709710559200349619912686075e+00, // N = 40
            0.990726238699457006453059775040808e+00,
            0.977259949983774262663372680946589e+00,
            0.957916819213791655804549152135004e+00,
            0.932812808278676533360846048743322e+00,
            0.902098806968874296728256187589215e+00,
            0.865959503212259503820780965880230e+00,
            0.824612230833311663196319386395722e+00,
            0.778305651426519387694971962275149e+00,
            0.727318255189927103280996392578681e+00,
            0.671956684614179548379354522018864e+00,
            0.612553889667980237952612446531931e+00,
            0.549467125095128202075931305770301e+00,
            0.483075801686178712908566574236461e+00,
            0.413779204371605001524879745802697e+00,
            0.341994090825758473007492481179385e+00,
            0.268152185007253681141184344808589e+00,
            0.192697580701371099715516852065149e+00,
            0.116084070675255208483451284408024e+00,
            0.387724175060508219331934440246233e-01,
            0.998321588574771441519208974223705e+00, // N = 41
            0.991167109699016308250070795872525e+00,
            0.978338673561083384469244077197344e+00,
            0.959906891730346226099368138818477e+00,
            0.935976987497853825682398798945039e+00,
            0.906685944758101172958298827319234e+00,
            0.872201511692441408833691024365248e+00,
            0.832721200401361331244265105957882e+00,
            0.788471145047409372736223583034500e+00,
            0.739704803069926181060168419345081e+00,
            0.686701502034951289584603909723612e+00,
            0.629764839072196320488649085698196e+00,
            0.569220941610215869654747216161481e+00,
            0.505416599199406032708336070154659e+00,
            0.438717277051407088517119856734970e+00,
            0.369505022640481441428366913299564e+00,
            0.298176277341824865922982880478940e+00,
            0.225139605633422775605786256655470e+00,
            0.150813354863992163574377967884582e+00,
            0.756232589891629969237661936512003e-01,
            0.0e+00,
            0.998399618990062415022927781463296e+00, // N = 42
            0.991577288340860919792218766893773e+00,
            0.979342508063748193709171838251135e+00,
            0.961759365338204488746722921393144e+00,
            0.938923557354988178533386869591188e+00,
            0.910959724904127452583733188528731e+00,
            0.878020569812172742712023103333721e+00,
            0.840285983261816900925422245716031e+00,
            0.797962053255487413232710909263336e+00,
            0.751279935689480489568470972524974e+00,
            0.700494590556171213741570111713478e+00,
            0.645883388869247833957496268800083e+00,
            0.587744597485109322840711350569167e+00,
            0.526395749931192287592867558134914e+00,
            0.462171912070421929759075029987511e+00,
            0.395423852042975057677093954590322e+00,
            0.326516124465411512197156589375750e+00,
            0.255825079342879083966414791018702e+00,
            0.183736806564854550852755639380743e+00,
            0.110645027208519868349122545002641e+00,
            0.369489431653517758130959800375594e-01,
            0.998472332242507713517763639617892e+00, // N = 43
            0.991959557593244146420361616318656e+00,
            0.980278220980255331506013186231257e+00,
            0.963486613014079993409717513624241e+00,
            0.941671956847637861818802068415789e+00,
            0.914947907206138729455924149718517e+00,
            0.883453765218616863337782686372492e+00,
            0.847353716209315048999052475209494e+00,
            0.806835964136938635279083799946392e+00,
            0.762111747194955121460326198457207e+00,
            0.713414235268957054851921116939796e+00,
            0.660997313751498133165134710481425e+00,
            0.605134259639600935725083076991443e+00,
            0.546116316660084719140405046318676e+00,
            0.484251176785734724069633434782990e+00,
            0.419861376029269252487279394553066e+00,
            0.353282612864303806645476364143826e+00,
            0.284861998032913627105722894838309e+00,
            0.214956244860518209014878381473676e+00,
            0.143929809510713310770299937610745e+00,
            0.721529908745862354223272509555611e-01,
            0.0e+00,
            0.998540200636774224936355443939961e+00, // N = 44
            0.992316392138515808482306011875058e+00,
            0.981151833077913966663437527062428e+00,
            0.965099650422493139393382794090751e+00,
            0.944239509118194099203856527684750e+00,
            0.918675259984175774322769738457655e+00,
            0.888534238286043202338519476279211e+00,
            0.853966595004710378728251826956267e+00,
            0.815144539645135010487459731669594e+00,
            0.772261479248755899017756368675330e+00,
            0.725531053660717002606965008108191e+00,
            0.675186070666122365333698962991269e+00,
            0.621477345903575847802424682655772e+00,
            0.564672453185470768424636824115519e+00,
            0.505054391388202317982798351852400e+00,
            0.442920174525411483834826593703385e+00,
            0.378579352014707132511764672767536e+00,
            0.312352466502785812236545163573171e+00,
            0.244569456928201251507302434740513e+00,
            0.175568014775516785746507749380977e+00,
            0.105691901708653247117305848915122e+00,
            0.352892369641353590581967046314164e-01,
            0.998603645181936638156031355247083e+00, // N = 45
            0.992649998447203741749363742306058e+00,
            0.981968715034540568237972057759374e+00,
            0.966608310396894604737431766398516e+00,
            0.946641690995629061783102829849021e+00,
            0.922163936719000388098076042261587e+00,
            0.893291671753241738463891463414798e+00,
            0.860162475960664225339297568328960e+00,
            0.822934220502086337035704554816386e+00,
            0.781784312593906291312379260687177e+00,
            0.736908848945490352623732483121861e+00,
            0.688521680771200525232021171270776e+00,
            0.636853394453223359271223635752016e+00,
            0.582150212569353186680967364814705e+00,
            0.524672820462916067091134097288075e+00,
            0.464695123919635098579601502651652e+00,
            0.402502943858541914077974508525513e+00,
            0.338392654250602161643404100032617e+00,
            0.272669769752377560608765391615597e+00,
            0.205647489783263745719787225471546e+00,
            0.137645205983253028756590041423066e+00,
            0.689869801631441724904146141038117e-01,
            0.0e+00,
            0.998663042133817981127427046421504e+00, // N = 46
            0.992962348906174364078142523089128e+00,
            0.982733669804166863472876038786077e+00,
            0.968021391853991942739896665098728e+00,
            0.948892363446089795618809025660387e+00,
            0.925433798806753950979356073504075e+00,
            0.897752711533941965699786051597052e+00,
            0.865975394866858062916349354759152e+00,
            0.830246837066066053032193245687497e+00,
            0.790730057075274255189208695420202e+00,
            0.747605359615666054000324297221213e+00,
            0.701069512020405697512125057096471e+00,
            0.651334846201997715106476748338911e+00,
            0.598628289712715153177172600332153e+00,
            0.543190330261802635270962686119799e+00,
            0.485273918388164662772320194180171e+00,
            0.425143313282828397322146863395939e+00,
            0.363072877020995710123706978517266e+00,
            0.299345822701870015483439256577863e+00,
            0.234252922206269768626056115573798e+00,
            0.168091179467103528606796737427702e+00,
            0.101162475305584239515859657008649e+00,
            0.337721900160520415195578318914398e-01,
            0.998718728584212109182415298766244e+00, // N = 47
            0.993255210987768634696250050789656e+00,
            0.983451003071623708761548014861543e+00,
            0.969346787326564497147555194965738e+00,
            0.951003969257708442587260525593985e+00,
            0.928502693012360648197752527188528e+00,
            0.901941329438525356866845665812779e+00,
            0.871436015796896316941142333462326e+00,
            0.837120139899902121277753985014452e+00,
            0.799143754167741942915549087247645e+00,
            0.757672918445438633574011872922301e+00,
            0.712888973409064301661875001616419e+00,
            0.664987747390332729136703621284670e+00,
            0.614178699956373608595462421641920e+00,
            0.560684005934664194483058321657156e+00,
            0.504737583863577919774289023290641e+00,
            0.446584073104855702725182142531500e+00,
            0.386477764084667139583302387593268e+00,
            0.324681486337735902210761299180695e+00,
            0.261465459214974570306982966205163e+00,
            0.197106110279111807961491358370503e+00,
            0.131884866554514897053823530724128e+00,
            0.660869239163556751604737774741337e-01,
            0.0e+00,
            0.998771007252426118605061865434257e+00, // N = 48
            0.993530172266350757533485837984753e+00,
            0.984124583722826857767990395796528e+00,
            0.970591592546247250436936111401991e+00,
            0.952987703160430860741457183259686e+00,
            0.931386690706554333100651991637703e+00,
            0.905879136715569672831101054759270e+00,
            0.876572020274247885901599188456379e+00,
            0.843588261624393530712786162293998e+00,
            0.807066204029442627081977356640102e+00,
            0.767159032515740339253991454499670e+00,
            0.724034130923814654674450332164464e+00,
            0.677872379632663905211855745698417e+00,
            0.628867396776513623995164326639663e+00,
            0.577224726083972703817809333348778e+00,
            0.523160974722233033678225863069105e+00,
            0.466902904750958404544928862038908e+00,
            0.408686481990716729916225495782758e+00,
            0.348755886292160738159817937271552e+00,
            0.287362487355455576735886461316879e+00,
            0.224763790394689061224865440174684e+00,
            0.161222356068891718056437390783498e+00,
            0.970046992094626989300539558536245e-01,
            0.323801709628693620333222431521344e-01,
            0.998820150606635379388377922370521e+00, // N = 49
            0.993788661944167790661804653715021e+00,
            0.984757895914213004515964508950160e+00,
            0.971762200901555380019912518394671e+00,
            0.954853658674137233653247569568534e+00,
            0.934100294755810149002284486628813e+00,
            0.909585655828073285248027792568303e+00,
            0.881408445573008910020122579228089e+00,
            0.849682119844165701040456938369208e+00,
            0.814534427359855431537883516496930e+00,
            0.776106894345446635018536987637700e+00,
            0.734554254237402696213588424826837e+00,
            0.690043824425132113504765771963895e+00,
            0.642754832419237664056855216227741e+00,
            0.592877694108900712455864523076351e+00,
            0.540613246991726066558225452023412e+00,
            0.486171941452492042176976096809091e+00,
            0.429772993341576524658584141773770e+00,
            0.371643501262284888863734540949220e+00,
            0.312017532119748762207860676505766e+00,
            0.251135178612577273507155942824625e+00,
            0.189241592461813586485310173859985e+00,
            0.126585997269672051067985288575536e+00,
            0.634206849826867860288348208784850e-01,
            0.0e+00,
            0.998866404420071050221644999046981e+00, // N = 50
            0.994031969432090712513288194570931e+00,
            0.985354084048005882464660736943510e+00,
            0.972864385106692073592033244567523e+00,
            0.956610955242807943085891706150152e+00,
            0.936656618944877933693444958897581e+00,
            0.913078556655791893129503150204595e+00,
            0.885967979523613048619125535861321e+00,
            0.855429769429946084620206390042546e+00,
            0.821582070859335948353463508147553e+00,
            0.784555832900399263905792879898874e+00,
            0.744494302226068538260429633235185e+00,
            0.701552468706822251089558191870754e+00,
            0.655896465685439360781622614603340e+00,
            0.607702927184950239180381642621237e+00,
            0.557158304514650054315522973417736e+00,
            0.504458144907464201651459121545089e+00,
            0.449806334974038789147131468739551e+00,
            0.393414311897565127394229253758021e+00,
            0.335500245419437356836988257294405e+00,
            0.276288193779531990327645278521138e+00,
            0.216007236876041756847284532617092e+00,
            0.154890589998145902071628620941110e+00,
            0.931747015600861408544503776396003e-01,
            0.310983383271888761123289896659492e-01,
            0.998909990848903495224033648428656e+00, // N = 51
            0.994261260436752574338102605940381e+00,
            0.985915991735902996976915842059536e+00,
            0.973903368019323866801093763881690e+00,
            0.958267848613908194856034517292444e+00,
            0.939067544002962383207157601720627e+00,
            0.916373862309780230926378548666742e+00,
            0.890271218029527303213730721913014e+00,
            0.860856711182292371484219707914386e+00,
            0.828239763823064832850725579237874e+00,
            0.792541712099381205235396753810856e+00,
            0.753895354485375525763787075691729e+00,
            0.712444457577036644580542793115430e+00,
            0.668343221175370086864466445393827e+00,
            0.621755704600723273755041382116644e+00,
            0.572855216351303836522394977743941e+00,
            0.521823669366185842514087749682147e+00,
            0.468850904286041063610457261750489e+00,
            0.414133983226303877936871809544767e+00,
            0.357876456688409509775201088533585e+00,
            0.300287606335331939530245649643412e+00,
            0.241581666447798703846733114869309e+00,
            0.181977026957077545323998701169213e+00,
            0.121695421018888766963820420963181e+00,
            0.609611001505787247341947068432054e-01,
            0.0e+00,
            0.998951111103950278018054699838196e+00, // N = 52
            0.994477590929216029684977516364457e+00,
            0.986446195651549840513947880332682e+00,
            0.974883884221744503438240575583190e+00,
            0.959831826933086552445972636330204e+00,
            0.941343853641359056710370283652786e+00,
            0.919486128916424539944189548698567e+00,
            0.894336890534495322515084505254327e+00,
            0.865986162846067585261432981503674e+00,
            0.834535432326734534963584819431080e+00,
            0.800097283430468324334317675212598e+00,
            0.762794995193744960279552606289236e+00,
            0.722762099749983193676624685627976e+00,
            0.680141904227167702092262345384622e+00,
            0.635086977695245924298119668638400e+00,
            0.587758604979579069902026675609997e+00,
            0.538326209285827438375951068446420e+00,
            0.486966745698096077782458249861024e+00,
            0.433864067718761670309086567803508e+00,
            0.379208269116093669246681766973017e+00,
            0.323195003434807825501099066597845e+00,
            0.266024783605001827472971730599104e+00,
            0.207902264156366059686466128122335e+00,
            0.149035508606949180488634040018114e+00,
            0.896352446489005654888546911223992e-01,
            0.299141097973387660436807760707999e-01,
            0.998989947776328227308717791212126e+00, // N = 53
            0.994681919308007078528606558174079e+00,
            0.986947035023371521606448472303821e+00,
            0.975810233714984582070103795268821e+00,
            0.961309694623136332403443517217904e+00,
            0.943495353464441879066821072026308e+00,
            0.922428603042812128061445320035148e+00,
            0.898182057875426625967237715458832e+00,
            0.870839297558241351480432015469135e+00,
            0.840494576545801375449789702087003e+00,
            0.807252498416895478215250648050254e+00,
            0.771227654925532307867136138137129e+00,
            0.732544230807510253781699199233659e+00,
            0.691335575601366723540834286889109e+00,
            0.647743743916510068751092141287791e+00,
            0.601919005713769327464295798295608e+00,
            0.554019328277067881014734994473705e+00,
            0.504209831657133437039116948768307e+00,
            0.452662219461845791383144763582231e+00,
            0.399554186953952977392563135999796e+00,
            0.345068808495722356694310646077604e+00,
            0.289393906451626206426547006593388e+00,
            0.232721403724272593643363642199913e+00,
            0.175246662155325750729791009132899e+00,
            0.117167809071955150140256808779324e+00,
            0.586850543002594650227119458332315e-01,
            0.0e+00,
            0.999026666867340983960600738628587e+00, // N = 54
            0.994875117018338883775009093857024e+00,
            0.987420637397343557973919278665868e+00,
            0.976686328857903238311316464892393e+00,
            0.962707645785923581151668047530001e+00,
            0.945530975164995855172690141891805e+00,
            0.925213359866651486227528234023990e+00,
            0.901822286284701580784300839998063e+00,
            0.875435454065568939184779288843327e+00,
            0.846140515970772949431093530994647e+00,
            0.814034785913567835453741271723255e+00,
            0.779224915346254021541712528523965e+00,
            0.741826538809184316284297613747209e+00,
            0.701963889719172919385857342339648e+00,
            0.659769387631983124692249575331223e+00,
            0.615383198331127370729942640361260e+00,
            0.568952768195209429731624518247519e+00,
            0.520632334385933073327017180610482e+00,
            0.470582412481382283683212143766264e+00,
            0.418969263255204528036102697110816e+00,
            0.365964340372191181984332108207166e+00,
            0.311743720834468228882550390148026e+00,
            0.256487520069997300077411214453172e+00,
            0.200379293606213569778602462829285e+00,
            0.143605427316256153947089762898790e+00,
            0.863545182632482152854431777687496e-01,
            0.288167481993417776562358475002271e-01,
            0.999061419564818541226167774833173e+00, // N = 55
            0.995057977847411877913032918602278e+00,
            0.987868941198889192607043771506083e+00,
            0.977515735503989211682648848405394e+00,
            0.964031328593135192583226925656829e+00,
            0.947458868041210743426703762384094e+00,
            0.927851424720791693935995813424644e+00,
            0.905271800744000027896859089109014e+00,
            0.879792322419895505895168143496562e+00,
            0.851494606617154471801946684813854e+00,
            0.820469298559320912382366530312199e+00,
            0.786815781127622365927101731712568e+00,
            0.750641856348021908669593465267489e+00,
            0.712063399986637838911033245145076e+00,
            0.671203990319826395796089591318945e+00,
            0.628194512249928140090660061053824e+00,
            0.583172738026032102974303596733496e+00,
            0.536282885908343296720599396946771e+00,
            0.487675158187474097208263700182115e+00,
            0.437505260037174591808481022197924e+00,
            0.385933900740979429755848544098330e+00,
            0.333126278890023885189471490218123e+00,
            0.279251553200806538549862451176431e+00,
            0.224482300647845483400189062402906e+00,
            0.168993963646873208282842493511703e+00,
            0.112964288059329266588437923888712e+00,
            0.565727538183367763273376108931084e-01,
            0.0e+00,
            0.999094343801465585752843252460937e+00, // N = 56
            0.995231226081069747987788275896544e+00,
            0.988293715540161499600551128237394e+00,
            0.978301709140256393942146980189338e+00,
            0.965285901905490181071368349173363e+00,
            0.949286479561962637900927761747548e+00,
            0.930352880247496298605517576768188e+00,
            0.908543620420655494331463136763581e+00,
            0.883926108327827539709415300466113e+00,
            0.856576433762748635992662052796269e+00,
            0.826579132142881651459993328593579e+00,
            0.794026922893866498085283636698268e+00,
            0.759020422705128902190324418393661e+00,
            0.721667834450188083526380135160209e+00,
            0.682084612694470455501089126837094e+00,
            0.640393106807006894268020252733450e+00,
            0.596722182770663320104126651392904e+00,
            0.551206824855534618754364367180926e+00,
            0.503987718384381714195224248753744e+00,
            0.455210814878459578948831595075495e+00,
            0.405026880927091278118866961613668e+00,
            0.353591032174954520969707327121873e+00,
            0.301062253867220669053094233119869e+00,
            0.247602909434337203972966554970932e+00,
            0.193378238635275258240184723012659e+00,
            0.138555846810376242012886580438492e+00,
            0.833051868224353744402873554406624e-01,
            0.277970352872754370940611967749205e-01,
            0.999125565625262853047052586618274e+00, // N = 57
            0.995395523678430309571007530945854e+00,
            0.988696577650222058093291260155730e+00,
            0.979047226709468710028855773441576e+00,
            0.966476085171886675206260428648027e+00,
            0.951020626447876751760081781501095e+00,
            0.932726961067101693313768901958825e+00,
            0.911649678521391216634801712415464e+00,
            0.887851678882221326547729121167007e+00,
            0.861403983262046944910565372183161e+00,
            0.832385521150439120956435312702651e+00,
            0.800882894547218242157003200042812e+00,
            0.766990119359450195497563539840781e+00,
            0.730808344744523322826905682560977e+00,
            0.692445551199517739040646304470458e+00,
            0.652016228280976891249368792302575e+00,
            0.609641032908715365423855156086652e+00,
            0.565446429269236759018985275962419e+00,
            0.519564311391187606315153809436177e+00,
            0.472131609517975709588060095348867e+00,
            0.423289881451563950960024350669576e+00,
            0.373184890086594458552134396251712e+00,
            0.321966168395378640590207915796013e+00,
            0.269786573161838765763345609800213e+00,
            0.216801828796124036413613975979514e+00,
            0.163170062591264251043280378321515e+00,
            0.109051332808787800978526521310979e+00,
            0.546071510016468242198305597373324e-01,
            0.0e+00,
            0.999155200407386632100251389048275e+00, // N = 58
            0.995551476597290867571702540506380e+00,
            0.989079008248442726803193205098877e+00,
            0.979755014694350216706933313565414e+00,
            0.967606202502924107423539738734020e+00,
            0.952667557518869048757370801891805e+00,
            0.934982137588259375374807917856005e+00,
            0.914600928564352547452654336836524e+00,
            0.891582692022030175339987617264199e+00,
            0.865993794074807480347599878281901e+00,
            0.837908013339373315981495773451357e+00,
            0.807406327913088141428533979896158e+00,
            0.774576681749652745172901784637459e+00,
            0.739513731020042267867800226405069e+00,
            0.702318571153908113474795784186639e+00,
            0.663098445332125266433888930045430e+00,
            0.621966435263079111033895970056397e+00,
            0.579041135130225030489993237012348e+00,
            0.534446309648847586399801286057781e+00,
            0.488310537216718463615552644198239e+00,
            0.440766839186839565193703058212541e+00,
            0.391952296330753150371216941733927e+00,
            0.342007653597995261248368267464475e+00,
            0.291076914311109189533025268314528e+00,
            0.239306924966153454428948509085552e+00,
            0.186846951835761321374383881464019e+00,
            0.133848250595466857022376847874542e+00,
            0.804636302141427293098477923805032e-01,
            0.268470123659423558033386895173800e-01,
            0.999183353909294667205643068296996e+00, // N = 59
            0.995699640383246036770413301974902e+00,
            0.989442365133730846475898804788999e+00,
            0.980427573956715736395688090400227e+00,
            0.968680221681781276638192932260919e+00,
            0.954233009376951119396793711348349e+00,
            0.937126190353453860057655556210748e+00,
            0.917407438788155306439449998259614e+00,
            0.895131711743472079740397219725958e+00,
            0.870361094292882260095209617544676e+00,
            0.843164625816872200475346743480618e+00,
            0.813618107288211571267677317694980e+00,
            0.781803889862360905697315286202025e+00,
            0.747810645278640231881518298098034e+00,
            0.711733118677197731596627763229656e+00,
            0.673671864504937227022507697048220e+00,
            0.633732966238850097512836105433795e+00,
            0.592027740704030144464136877018302e+00,
            0.548672427808396384372261769039267e+00,
            0.503787866557717978768086422389926e+00,
            0.457499158253266690226215335874941e+00,
            0.409935317810418966722823687397087e+00,
            0.361228914169794809992312452701368e+00,
            0.311515700803013700318360149087415e+00,
            0.260934237342811711610616267415249e+00,
            0.209625503392036544923366790631453e+00,
            0.157732505587857968115217856271556e+00,
            0.105399879016344143836914387761869e+00,
            0.527734840883100039516803286033385e-01,
            0.0e+00,
            0.999210123227435862070008493811879e+00, // N = 60
            0.995840525118838493161148614181831e+00,
            0.989787895222221271450482647400812e+00,
            0.981067201752599008939885831067381e+00,
            0.969701788765052248615160049552028e+00,
            0.955722255839996509135760625432896e+00,
            0.939166276116422948124242613231917e+00,
            0.920078476177627688588783024338264e+00,
            0.898510310810045898328277872176401e+00,
            0.874519922646898344644990343709189e+00,
            0.848171984785929627768557743110825e+00,
            0.819537526162145759257030139576634e+00,
            0.788693739932264054658845269983062e+00,
            0.755723775306585686849000838727920e+00,
            0.720716513355730399465937730737008e+00,
            0.683766327381355437214531572791347e+00,
            0.644972828489477067814990715855943e+00,
            0.604440597048510363444040497186835e+00,
            0.562278900753944539178290960157120e+00,
            0.518601400058569747417888018230881e+00,
            0.473525841761707111108163217027638e+00,
            0.427173741583078389307452839032456e+00,
            0.379670056576797977154952671049762e+00,
            0.331142848268448194252352965359391e+00,
            0.281722937423261691690694860338387e+00,
            0.231543551376029338010344631347002e+00,
            0.180739964873425417240876941261828e+00,
            0.129449135396945003146444164649577e+00,
            0.778093339495365694192855070822253e-01,
            0.259597723012477985891703854003448e-01,
            0.999235597631363693039497410657766e+00, // N = 61
            0.995974599815119342263598364501092e+00,
            0.990116745232519013636920116523524e+00,
            0.981676011284034567431767468750177e+00,
            0.970674258833184712990754217961157e+00,
            0.957140151912982705966175662483687e+00,
            0.941108986681361549300197756536372e+00,
            0.922622581382954797720565952303437e+00,
            0.901729162474001419858887789619907e+00,
            0.878483237214880895287229014520398e+00,
            0.852945450847663489990814389171189e+00,
            0.825182428108659939301652112000031e+00,
            0.795266599282359652947553914700569e+00,
            0.763276011172312195999923999232898e+00,
            0.729294123449465109938543089998003e+00,
            0.693409590894491155459373831275755e+00,
            0.655716032095070871706527268032628e+00,
            0.616311785197921724708389601544512e+00,
            0.575299651350830618600472826084821e+00,
            0.532786626502925265638471578622534e+00,
            0.488883622262252118820699181845782e+00,
            0.443705176538531601995589259889052e+00,
            0.397369154725756609178291851404222e+00,
            0.349996442204066834533434476861401e+00,
            0.301710628963030712604486525466729e+00,
            0.252637687169053495833690863334470e+00,
            0.202905642518058499226947203343037e+00,
            0.152644240230815300529506761773480e+00,
            0.101984606562274068957208404764366e+00,
            0.510589067079743493668875006189008e-01,
            0.0e+00
        };

        public static readonly double[] GaussWeight =
        {
            0.0e+00,
            0.200000000000000000000000000000000e+01, // N = 1
            0.100000000000000000000000000000000e+01, // N = 2
            0.555555555555555555555555555555555e+00, // N = 3
            0.888888888888888888888888888888889e+00,
            0.347854845137453857373063949221999e+00, // N = 4
            0.652145154862546142626936050778001e+00,
            0.236926885056189087514264040719917e+00, // N = 5
            0.478628670499366468041291514835638e+00,
            0.568888888888888888888888888888889e+00,
            0.171324492379170345040296142172733e+00, // N = 6
            0.360761573048138607569833513837716e+00,
            0.467913934572691047389870343989551e+00,
            0.129484966168869693270611432679083e+00, // N = 7
            0.279705391489276667901467771423778e+00,
            0.381830050505118944950369775488978e+00,
            0.417959183673469387755102040816324e+00,
            0.101228536290376259152531354309963e+00, // N = 8
            0.222381034453374470544355994426239e+00,
            0.313706645877887287337962201986603e+00,
            0.362683783378361982965150449277195e+00,
            0.812743883615744119718921581105244e-01, // N = 9
            0.180648160694857404058472031242912e+00,
            0.260610696402935462318742869418636e+00,
            0.312347077040002840068630406584444e+00,
            0.330239355001259763164525069286978e+00,
            0.666713443086881375935688098933317e-01, // N = 10
            0.149451349150580593145776339657693e+00,
            0.219086362515982043995534934228166e+00,
            0.269266719309996355091226921569470e+00,
            0.295524224714752870173892994651339e+00,
            0.556685671161736664827537204425497e-01, // N = 11
            0.125580369464904624634694299223937e+00,
            0.186290210927734251426097641431661e+00,
            0.233193764591990479918523704843169e+00,
            0.262804544510246662180688869890515e+00,
            0.272925086777900630714483528336339e+00,
            0.471753363865118271946159614850133e-01, // N = 12
            0.106939325995318430960254718194013e+00,
            0.160078328543346226334652529543347e+00,
            0.203167426723065921749064455809812e+00,
            0.233492536538354808760849898924877e+00,
            0.249147045813402785000562436042951e+00,
            0.404840047653158795200215922009913e-01, // N = 13
            0.921214998377284479144217759538088e-01,
            0.138873510219787238463601776868882e+00,
            0.178145980761945738280046691996084e+00,
            0.207816047536888502312523219306048e+00,
            0.226283180262897238412090186039811e+00,
            0.232551553230873910194589515268787e+00,
            0.351194603317518630318328761381690e-01, // N = 14
            0.801580871597602098056332770628825e-01,
            0.121518570687903184689414809072460e+00,
            0.157203167158193534569601938623896e+00,
            0.185538397477937813741716590125112e+00,
            0.205198463721295603965924065661222e+00,
            0.215263853463157790195876443316267e+00,
            0.307532419961172683546283935771943e-01, // N = 15
            0.703660474881081247092674164506892e-01,
            0.107159220467171935011869546685734e+00,
            0.139570677926154314447804794511208e+00,
            0.166269205816993933553200860480891e+00,
            0.186161000015562211026800561866565e+00,
            0.198431485327111576456118326443407e+00,
            0.202578241925561272880620199967656e+00,
            0.271524594117540948517805724560368e-01, // N = 16
            0.622535239386478928628438369945628e-01,
            0.951585116824927848099251076018181e-01,
            0.124628971255533872052476282192097e+00,
            0.149595988816576732081501730547117e+00,
            0.169156519395002538189312079030817e+00,
            0.182603415044923588866763667969201e+00,
            0.189450610455068496285396723208291e+00,
            0.241483028685479319601100262874223e-01, // N = 17
            0.554595293739872011294401653581783e-01,
            0.850361483171791808835353701908650e-01,
            0.111883847193403971094788385627117e+00,
            0.135136368468525473286319981701965e+00,
            0.154045761076810288081431594801964e+00,
            0.168004102156450044509970663788286e+00,
            0.176562705366992646325270990114256e+00,
            0.179446470356206525458265644261812e+00,
            0.216160135264833103133427102655130e-01, // N = 18
            0.497145488949697964533349462010895e-01,
            0.764257302548890565291296776163320e-01,
            0.100942044106287165562813984928046e+00,
            0.122555206711478460184519126798015e+00,
            0.140642914670650651204731303753862e+00,
            0.154684675126265244925418003835190e+00,
            0.164276483745832722986053776466578e+00,
            0.169142382963143591840656470134736e+00,
            0.194617882297264770363120414644793e-01, // N = 19
            0.448142267656996003328381574039431e-01,
            0.690445427376412265807082579987094e-01,
            0.914900216224499994644620941319334e-01,
            0.111566645547333994716023901674946e+00,
            0.128753962539336227675515784862361e+00,
            0.142606702173606611775746109431414e+00,
            0.152766042065859666778855400902497e+00,
            0.158968843393954347649956439460513e+00,
            0.161054449848783695979163625324809e+00,
            0.176140071391521183118619623491302e-01, // N = 20
            0.406014298003869413310399522706322e-01,
            0.626720483341090635695065351819669e-01,
            0.832767415767047487247581432329156e-01,
            0.101930119817240435036750135466348e+00,
            0.118194531961518417312377377718604e+00,
            0.131688638449176626898494499748159e+00,
            0.142096109318382051329298325072027e+00,
            0.149172986472603746787828736999336e+00,
            0.152753387130725850698084331956079e+00,
            0.160172282577743333242246168579398e-01, // N = 21
            0.369537897708524937999506683027812e-01,
            0.571344254268572082836358264526385e-01,
            0.761001136283793020170516533126966e-01,
            0.934444234560338615532897410907539e-01,
            0.108797299167148377663474578081143e+00,
            0.121831416053728534195367177105957e+00,
            0.132268938633337461781052574507564e+00,
            0.139887394791073154722133423860591e+00,
            0.144524403989970059063827166570068e+00,
            0.146081133649690427191985147672526e+00,
            0.146279952982722006849910980409279e-01, // N = 22
            0.337749015848141547933022468735675e-01,
            0.522933351526832859403120512609446e-01,
            0.697964684245204880949614189253340e-01,
            0.859416062170677274144436813628141e-01,
            0.100414144442880964932078837856422e+00,
            0.112932296080539218393400607417128e+00,
            0.123252376810512424285560986159639e+00,
            0.131173504787062370732964992516422e+00,
            0.136541498346015171352573831229592e+00,
            0.139251872855631993375410248339356e+00,
            0.134118594871417720813094934295282e-01, // N = 23
            0.309880058569794443106942196749048e-01,
            0.480376717310846685716410715037491e-01,
            0.642324214085258521271696153694344e-01,
            0.792814117767189549228925246444880e-01,
            0.929157660600351474770186174421938e-01,
            0.104892091464541410074086184918183e+00,
            0.114996640222411364941643512970691e+00,
            0.123049084306729530467578400635032e+00,
            0.128905722188082149978595339377180e+00,
            0.132462039404696617371642464587308e+00,
            0.133654572186106175351457110560180e+00,
            0.123412297999871995468056670241292e-01, // N = 24
            0.285313886289336631813078161424755e-01,
            0.442774388174198061686027483473371e-01,
            0.592985849154367807463677585232428e-01,
            0.733464814110803057340336151500117e-01,
            0.861901615319532759171852029475615e-01,
            0.976186521041138882698806644404639e-01,
            0.107444270115965634782577342387576e+00,
            0.115505668053725601353344483876487e+00,
            0.121670472927803391204463153443133e+00,
            0.125837456346828296121375382504667e+00,
            0.127938195346752156974056165213338e+00,
            0.113937985010262879479029641285760e-01, // N = 25
            0.263549866150321372619018153849308e-01,
            0.409391567013063126556234878061658e-01,
            0.549046959758351919259368913429170e-01,
            0.680383338123569172071871854580119e-01,
            0.801407003350010180132349597253873e-01,
            0.910282619829636498114972206076789e-01,
            0.100535949067050644202206890357531e+00,
            0.108519624474263653116093957004116e+00,
            0.114858259145711648339325546015923e+00,
            0.119455763535784772228178126428148e+00,
            0.122242442990310041688959518496597e+00,
            0.123176053726715451203902872852701e+00,
            0.105513726173430071556511877104122e-01, // N = 26
            0.244178510926319087896158276999699e-01,
            0.379623832943627639503031403683517e-01,
            0.509758252971478119983199014950844e-01,
            0.632740463295748355394536886745920e-01,
            0.746841497656597458870757954790540e-01,
            0.850458943134852392104477650671504e-01,
            0.942138003559141484636648834149007e-01,
            0.102059161094425423238414070130089e+00,
            0.108471840528576590656579427177621e+00,
            0.113361816546319666549440718687763e+00,
            0.116660443485296582044662507678498e+00,
            0.118321415279262276516371085754385e+00,
            0.979899605129436026115005491579836e-02, // N = 27
            0.226862315961806231960342068377974e-01,
            0.352970537574197110225782887373276e-01,
            0.474494125206150627040967109638731e-01,
            0.589835368598335991103008321613220e-01,
            0.697488237662455929843228905700173e-01,
            0.796048677730577712630749569057360e-01,
            0.884231585437569501943228042686763e-01,
            0.960887273700285075656526456436726e-01,
            0.102501637817745798671247711893808e+00,
            0.107578285788533187212162982779084e+00,
            0.111252488356845192672163097383528e+00,
            0.113476346108965148620369947144452e+00,
            0.114220867378956989045045738642052e+00,
            0.912428259309451773881615569631855e-02, // N = 28
            0.211321125927712597515003812942859e-01,
            0.329014277823043799776308250272362e-01,
            0.442729347590042278395878813243135e-01,
            0.551073456757167454314829123943426e-01,
            0.652729239669995957933975656147100e-01,
            0.746462142345687790239318849300299e-01,
            0.831134172289012183903964990431992e-01,
            0.905717443930328409421860308063307e-01,
            0.969306579979299158504890075865571e-01,
            0.102112967578060769814216637758528e+00,
            0.106055765922846417910416436445329e+00,
            0.108711192258294135253571519592793e+00,
            0.110047013016475196282376265548836e+00,
            0.851690387874640965426381577347572e-02, // N = 29
            0.197320850561227059838597996078192e-01,
            0.307404922020936226444085265013693e-01,
            0.414020625186828361048300262229884e-01,
            0.515948269024979239125943704172896e-01,
            0.612030906570791385421098602186590e-01,
            0.701179332550512785695814722557421e-01,
            0.782383271357637838281448972399983e-01,
            0.854722573661725275453448395871070e-01,
            0.917377571392587633479664164699553e-01,
            0.969638340944086063019000669506585e-01,
            0.101091273759914966121820571365711e+00,
            0.104073310077729373913328459501218e+00,
            0.105876155097320941406591333879246e+00,
            0.106479381718314244246511117763216e+00,
            0.796819249616660561546588320979440e-02, // N = 30
            0.184664683110909591423021417545798e-01,
            0.287847078833233693497191334338105e-01,
            0.387991925696270495968019675782981e-01,
            0.484026728305940529029380877991328e-01,
            0.574931562176190664817217211374840e-01,
            0.659742298821804951281285021811915e-01,
            0.737559747377052062682438639500205e-01,
            0.807558952294202153546949312507312e-01,
            0.868997872010829798023875393459500e-01,
            0.921225222377861287176326950378307e-01,
            0.963687371746442596394686287290119e-01,
            0.995934205867952670627802782841594e-01,
            0.101762389748405504596428957296642e+00,
            0.102852652893558840341285636117340e+00,
            0.747083157924877585869687724099065e-02, // N = 31
            0.173186207903105824631580131765678e-01,
            0.270090191849794218006086595184583e-01,
            0.364322739123854640243921219453832e-01,
            0.454937075272011029023157967071035e-01,
            0.541030824249168537116662949074201e-01,
            0.621747865610284269103434659239060e-01,
            0.696285832354103661677561766299470e-01,
            0.763903865987766164263576828237694e-01,
            0.823929917615892639038233996447944e-01,
            0.875767406084778761261980322803715e-01,
            0.918901138936414782153629019034390e-01,
            0.952902429123195128072042280005919e-01,
            0.977433353863287250934740272289929e-01,
            0.992250112266723078748754708406477e-01,
            0.997205447934264514275338784839920e-01,
            0.701861000947009660040713138619486e-02, // N = 32
            0.162743947309056706051705049405647e-01,
            0.253920653092620594557524998697045e-01,
            0.342738629130214331026878628853265e-01,
            0.428358980222266806568785625642849e-01,
            0.509980592623761761961633753381200e-01,
            0.586840934785355471452834724909903e-01,
            0.658222227763618468376501454904681e-01,
            0.723457941088485062253992440937225e-01,
            0.781938957870703064717410114205194e-01,
            0.833119242269467552221989835884973e-01,
            0.876520930044038111427715633570701e-01,
            0.911738786957638847128685539410870e-01,
            0.938443990808045656391802300089055e-01,
            0.956387200792748594190819835027716e-01,
            0.965400885147278005667648306528438e-01,
            0.660622784758737805864922877032642e-02, // N = 33
            0.153217015129346761279457699345655e-01,
            0.239155481017494803505328778505850e-01,
            0.323003586323289532815615102104468e-01,
            0.404015413316695915634093067002850e-01,
            0.481477428187116956701472176098583e-01,
            0.554708466316635612849440094479191e-01,
            0.623064825303174800316279007854007e-01,
            0.685945728186567128059549594976362e-01,
            0.742798548439541493424721583967375e-01,
            0.793123647948867383639082229650415e-01,
            0.836478760670387076139281584870639e-01,
            0.872482876188443376072816466707219e-01,
            0.900819586606385772397440656587539e-01,
            0.921239866433168462132407122899904e-01,
            0.933564260655961161609991257678634e-01,
            0.937684461602099965673045293923944e-01,
            0.622914055590868471860637566866174e-02, // N = 34
            0.144501627485950354152009896359124e-01,
            0.225637219854949700840939054778768e-01,
            0.304913806384461318094427429868726e-01,
            0.381665937963875163217654285664198e-01,
            0.455256115233532724538225886938685e-01,
            0.525074145726781061682465130210517e-01,
            0.590541358275244931939610038625709e-01,
            0.651115215540764113785448590388010e-01,
            0.706293758142557249990390436899042e-01,
            0.755619746600319312708340588066969e-01,
            0.798684443397718447388186740901156e-01,
            0.835130996998456551870202301621027e-01,
            0.864657397470357497842467160803940e-01,
            0.887018978356938692870764646651528e-01,
            0.902030443706407295739421994186261e-01,
            0.909567403302598736153376232912413e-01,
            0.588343342044308497575394315283040e-02, // N = 35
            0.136508283483614922664043342489063e-01,
            0.213229799114835808834381716542737e-01,
            0.288292601088942540487152733461378e-01,
            0.361101158634633805327183978252812e-01,
            0.431084223261702187823070359497274e-01,
            0.497693704013535298051999699259647e-01,
            0.560408162123701285783277091891905e-01,
            0.618736719660801888870137944366278e-01,
            0.672222852690869039643056733370462e-01,
            0.720447947725600646654621467061200e-01,
            0.763034571554420535386588459730511e-01,
            0.799649422423242629326628121726383e-01,
            0.830005937288565883799264208370588e-01,
            0.853866533920991252259436672251274e-01,
            0.871044469971835342433215048001668e-01,
            0.881405304302754629707399355550232e-01,
            0.884867949071042906382070005983414e-01,
            0.556571966424504536125579260204086e-02, // N = 36
            0.129159472840655744045072673326750e-01,
            0.201815152977354715320927002754055e-01,
            0.272986214985687790944198123801949e-01,
            0.342138107703072299212416121536277e-01,
            0.408757509236448954741132294083114e-01,
            0.472350834902659784166141564033446e-01,
            0.532447139777599190920283623401153e-01,
            0.588601442453248173096729710098699e-01,
            0.640397973550154895563852212861955e-01,
            0.687453238357364426136897547484451e-01,
            0.729418850056530613538736418755875e-01,
            0.765984106458706745287581499737530e-01,
            0.796878289120716019087254535846620e-01,
            0.821872667043397095172231121156339e-01,
            0.840782189796619349334581192102230e-01,
            0.853466857393386274918504399709375e-01,
            0.859832756703947474900850736892054e-01,
            0.527305727949793935172120296846413e-02, // N = 37
            0.122387801003075565263037796234417e-01,
            0.191290444890839660435089980042715e-01,
            0.258860369905589335227547710993802e-01,
            0.324616398475214810672384195936448e-01,
            0.388096025019345444889564332644499e-01,
            0.448853646624371666574093504318489e-01,
            0.506462976548246016038747992579043e-01,
            0.560519879982749178085412831679986e-01,
            0.610645165232259861309883138115698e-01,
            0.656487228727512494840274587897768e-01,
            0.697724515557003448850801367999320e-01,
            0.734067772484881727246224102940733e-01,
            0.765262075705292378858920668768501e-01,
            0.791088618375293807671991171762515e-01,
            0.811366245084650305098821274394437e-01,
            0.825952722364372508912355821254682e-01,
            0.834745736258627872522587327112268e-01,
            0.837683609931389047970120750514186e-01,
            0.500288074963934567590309956852149e-02, // N = 38
            0.116134447164686741776836569482318e-01,
            0.181565777096132368988901530206269e-01,
            0.245797397382323758952263713380185e-01,
            0.308395005451750546587452031620245e-01,
            0.368940815940247381649360656714863e-01,
            0.427031585046744342358668987964580e-01,
            0.482280618607586833743486085881141e-01,
            0.534320199103323199737476194657398e-01,
            0.582803991469972060223085829895579e-01,
            0.627409333921330540529606267321689e-01,
            0.667839379791404119350464003530889e-01,
            0.703825070668989547392868130219115e-01,
            0.735126925847434571452095691532865e-01,
            0.761536635484463960659894510856273e-01,
            0.782878446582109480753799305149081e-01,
            0.799010332435278215860273758642986e-01,
            0.809824937705971006232679716771238e-01,
            0.815250292803857866992189289704692e-01,
            0.475294469163510137077675042087210e-02, // N = 39
            0.110347889391645942426517991847001e-01,
            0.172562290937249190408182314077432e-01,
            0.233693848321781645946794838363440e-01,
            0.293349559839033785922222175997544e-01,
            0.351151114981313307610193904406787e-01,
            0.406732768479338439390883512150343e-01,
            0.459743011089166318841449405362516e-01,
            0.509846652921294052140690848096193e-01,
            0.556726903409162999073374707336450e-01,
            0.600087360885961495749664671970510e-01,
            0.639653881386823889866938650319631e-01,
            0.675176309662312653630260693196325e-01,
            0.706430059706087607701032020461776e-01,
            0.733217534142686173811548189969739e-01,
            0.755369373228360577047663382744344e-01,
            0.772745525446820167285397935609001e-01,
            0.785236132873711767250522140644442e-01,
            0.792762225683684710101498006273823e-01,
            0.795276221394428524173872204443145e-01,
            0.452127709853319125848508507294927e-02, // N = 40
            0.104982845311528136146364668266440e-01,
            0.164210583819078887127423380858061e-01,
            0.222458491941669572614516733163778e-01,
            0.279370069800234010983476020081574e-01,
            0.334601952825478473927707444428111e-01,
            0.387821679744720176399133018691669e-01,
            0.438709081856732719916865354815208e-01,
            0.486958076350722320614617038823308e-01,
            0.532278469839368243549451826570061e-01,
            0.574397690993915513666228321544156e-01,
            0.613062424929289391666009097335414e-01,
            0.648040134566010380745416592730193e-01,
            0.679120458152339038256953754182832e-01,
            0.706116473912867796955265510162431e-01,
            0.728865823958040590605108606145731e-01,
            0.747231690579682642001919898117514e-01,
            0.761103619006262423715663560707229e-01,
            0.770398181642479655883089525855804e-01,
            0.775059479784248112637240717735455e-01,
            0.430614035816488768394588393952231e-02, // N = 41
            0.999993877390594533848901042958917e-02,
            0.156449384078185885306890867122376e-01,
            0.212010633687795530758895427770357e-01,
            0.266358992071104454671075370931667e-01,
            0.319182117316992817873724972366412e-01,
            0.370177167035079884349098521818212e-01,
            0.419051951959096894296482462956402e-01,
            0.465526483690143420605964350660644e-01,
            0.509334542946174947813255440273393e-01,
            0.550225192425787418798644118799982e-01,
            0.587964209498719449913118102024445e-01,
            0.622335425809663164715147643899562e-01,
            0.653141964535274104363301435558487e-01,
            0.680207367608767667353948358293654e-01,
            0.703376606208174974816595826741789e-01,
            0.722516968610230733960874867779371e-01,
            0.737518820272234699393644210384210e-01,
            0.748296231762215518910063525757063e-01,
            0.754787470927158240273606390378492e-01,
            0.756955356472983723187038409958360e-01,
            0.410599860464908461061023555717252e-02, // N = 42
            0.953622030174850241218140290025007e-02,
            0.149224436973574941444470887695989e-01,
            0.202278695690526447574727038771351e-01,
            0.254229595261130478859924599653188e-01,
            0.304792406996034683638741770807150e-01,
            0.353690710975921108321682649311524e-01,
            0.400657351806922617612268859168247e-01,
            0.445435777719658778735942286930957e-01,
            0.487781407928032450279671059065116e-01,
            0.527462956991740703436828380965317e-01,
            0.564263693580183816468350876909122e-01,
            0.597982622275866543127356220087449e-01,
            0.628435580450025764095778274276134e-01,
            0.655456243649089789266190558161060e-01,
            0.678897033765219448554488795494112e-01,
            0.698629924925941597661171952026983e-01,
            0.714547142651709829218466852761936e-01,
            0.726561752438041048878376912508503e-01,
            0.734608134534675282640391984885782e-01,
            0.738642342321728799963637691291260e-01,
            0.391949025384412728301313370513146e-02, // N = 43
            0.910399663740140331903898555973831e-02,
            0.142487564315764861087398564566926e-01,
            0.193199014236839003968433523619754e-01,
            0.242904566138388159005474613894009e-01,
            0.291344132614984949169565674050855e-01,
            0.338264920868602923435993731945424e-01,
            0.383422221941326575737094433063429e-01,
            0.426580571979820837626126510734454e-01,
            0.467514947543465800116196327922125e-01,
            0.506011927843901565228717483571105e-01,
            0.541870803188817868646377209701441e-01,
            0.574904619569105194267933125719596e-01,
            0.604941152499912945204986825844190e-01,
            0.631823804493961123252851197622471e-01,
            0.655412421263227974928592788838597e-01,
            0.675584022293651691916040212965895e-01,
            0.692233441936566842823596175388094e-01,
            0.705273877650850281257416306096107e-01,
            0.714637342525141412981403060607628e-01,
            0.720275019714219743452997245576738e-01,
            0.722157516937989879783014072636609e-01,
            0.374540480311277751558668544586289e-02, // N = 44
            0.870048136752484411830559190599793e-02,
            0.136195867555799855230599173946368e-01,
            0.184714817368147491745923238895006e-01,
            0.232314819020192106292483479722854e-01,
            0.278757828212810100829517099944164e-01,
            0.323812228120698208767462203957668e-01,
            0.367253478138088736445557986189477e-01,
            0.408865123103462189040366252645304e-01,
            0.448439840819700314490116191019649e-01,
            0.485780464483520375277895043812568e-01,
            0.520700960917044618838249621676542e-01,
            0.553027355637280525467830929029284e-01,
            0.582598598775954953347783108211369e-01,
            0.609267367015619680364045420889898e-01,
            0.632900797332038549513215120354114e-01,
            0.653381148791814349829448549870313e-01,
            0.670606389062936523961369993025657e-01,
            0.684490702693666609851969949400314e-01,
            0.694964918615725780375803971548750e-01,
            0.701976854735582125870852277180351e-01,
            0.705491577893540688113908942761203e-01,
            0.358266315528355892950758360217166e-02, // N = 45
            0.832318929621824164697409358684734e-02,
            0.130311049915827843220561191507863e-01,
            0.176775352579375906107782182906942e-01,
            0.222398475505787323930046829556212e-01,
            0.266962139675776648049642257811481e-01,
            0.310253749345154671638784990684112e-01,
            0.352066922016090162477729047931937e-01,
            0.392202367293024475681754804365179e-01,
            0.430468807091649711524038030190039e-01,
            0.466683877183733652717098312249616e-01,
            0.500674992379520297909930394489517e-01,
            0.532280167312689519510336910119930e-01,
            0.561348787597864766410766341721373e-01,
            0.587742327188417385772191795687547e-01,
            0.611335008310665224992878345641582e-01,
            0.632014400738199377530918242800216e-01,
            0.649681957507234308533555512203219e-01,
            0.664253484498425280911339334753702e-01,
            0.675659541636075362708739476615854e-01,
            0.683845773786696745330090234556449e-01,
            0.688773169776613228805591571728431e-01,
            0.690418248292320201111524467703311e-01,
            0.343030086810704828642591584204214e-02, // N = 46
            0.796989822972462246425032227433478e-02,
            0.124798837709886841840621348806185e-01,
            0.169335140078362380501085020830833e-01,
            0.213099987541365010481533734035053e-01,
            0.255892863971300106300339893464403e-01,
            0.297518295522027558124601845315550e-01,
            0.337786279991068965126618016297720e-01,
            0.376513053573860713413554183915490e-01,
            0.413521901096787296881730806590433e-01,
            0.448643952773181267666818700675079e-01,
            0.481718951017122005223525166184401e-01,
            0.512595980071430213420289666520494e-01,
            0.541134153858567544899943990877935e-01,
            0.567203258439912358189601545343214e-01,
            0.590684345955463148015173560040283e-01,
            0.611470277246504810237160589363533e-01,
            0.629466210643945081752876595999599e-01,
            0.644590034671390695897601195774562e-01,
            0.656772742677812073771971814716057e-01,
            0.665958747684548873784014384472066e-01,
            0.672106136006781758628359124722649e-01,
            0.675186858490364588202031319579642e-01,
            0.328745384252801487898311676209319e-02, // N = 47
            0.763861629584883360846339404425152e-02,
            0.119628484643123209613632008321552e-01,
            0.162353331464330596673765255916666e-01,
            0.204369381476684276319063978515533e-01,
            0.245492116596588185215713425365295e-01,
            0.285541507006433864965886921571564e-01,
            0.324342355151847567612709713614516e-01,
            0.361724965841749516324196621878303e-01,
            0.397525861225310037587460580247897e-01,
            0.431588486484795382587366872405725e-01,
            0.463763890865059112269278110160970e-01,
            0.493911377473611695938167194472575e-01,
            0.521899117800571448614008820293490e-01,
            0.547604727815302259634624240499499e-01,
            0.570915802932315402247166706047302e-01,
            0.591730409423388759822494087284767e-01,
            0.609957530087396453316863886823380e-01,
            0.625517462209216626482915091386668e-01,
            0.638342166057170306275769226649446e-01,
            0.648375562389457267154464097578265e-01,
            0.655573777665497402366218607238262e-01,
            0.659905335888104745223628873358430e-01,
            0.661351296236554796553378625290386e-01,
            0.315334605230583862368239796468966e-02, // N = 48
            0.732755390127626210482494385417413e-02,
            0.114772345792345394876558926395461e-01,
            0.155793157229438487825975647427245e-01,
            0.196161604573555277868723719155527e-01,
            0.235707608393243791436801370538744e-01,
            0.274265097083569480717107372624816e-01,
            0.311672278327980889659588180242818e-01,
            0.347772225647704388364694926767587e-01,
            0.382413510658307063980450043607073e-01,
            0.415450829434647491603841511752491e-01,
            0.446745608566942804896973337543355e-01,
            0.476166584924904747862626457488802e-01,
            0.503590355538544749631023414365430e-01,
            0.528901894851936670893200120166696e-01,
            0.551995036999841628953878251461178e-01,
            0.572772921004032156911637671817087e-01,
            0.591148396983956357594672881911607e-01,
            0.607044391658938800203930296862858e-01,
            0.620394231598926639107670112310605e-01,
            0.631141922862540256440434320324953e-01,
            0.639242385846481866345893229648291e-01,
            0.644661644359500822013881893167522e-01,
            0.647376968126839225045888321571501e-01,
            0.302727898892290510561231777613290e-02, // N = 49
            0.703509959008645137354965995563251e-02,
            0.110205510315935805166517377514429e-01,
            0.149621449356246510635856987732352e-01,
            0.188435958530894580085220759791957e-01,
            0.226492015874466766465196542585839e-01,
            0.263636189270660165647996295505485e-01,
            0.299718846205838254945889782178363e-01,
            0.334594667916221741130469643735188e-01,
            0.368123209630006901836590905024859e-01,
            0.400169457663730211664189759018262e-01,
            0.430604369812595982872652208669184e-01,
            0.459305393555958533614819312390256e-01,
            0.486156958878282405019522327602869e-01,
            0.511050943301445904501815002464393e-01,
            0.533887107082589687587154970297695e-01,
            0.554573496748035884888408982388678e-01,
            0.573026815301874757128287200583188e-01,
            0.589172757600272657385249712130531e-01,
            0.602946309531520175669294852905813e-01,
            0.614292009791929359872785217402887e-01,
            0.623164173200572675182374705251817e-01,
            0.629527074651956992712079615892779e-01,
            0.633355092964917487602573446308019e-01,
            0.634632814047905976070859561671424e-01,
            0.290862255315514094172472914505657e-02, // N = 50
            0.675979919574540167926474544526016e-02,
            0.105905483836509689242872255474178e-01,
            0.143808227614855742261641383116087e-01,
            0.181155607134893895230313249790650e-01,
            0.217802431701247930256455674224051e-01,
            0.253606735700123897117859563343183e-01,
            0.288429935805351980911187546390511e-01,
            0.322137282235780163633237054970370e-01,
            0.354598356151461542859558743555247e-01,
            0.385687566125876749237823178407772e-01,
            0.415284630901476978226912114495093e-01,
            0.443275043388032752912251732594724e-01,
            0.469550513039484329578982512899774e-01,
            0.494009384494663147920769360809172e-01,
            0.516557030695811386864773425606938e-01,
            0.537106218889962464339854529760055e-01,
            0.555577448062125177224591249057815e-01,
            0.571899256477283835240727766218481e-01,
            0.586008498132224459085195503254319e-01,
            0.597850587042654574514555793402422e-01,
            0.607379708417702160700874680495243e-01,
            0.614558995903166636772026154856285e-01,
            0.619360674206832433834351848662688e-01,
            0.621766166553472623205770905078938e-01,
            0.279680717108989546216606954644902e-02, // N = 51
            0.650033778325259969307060260560534e-02,
            0.101851912978217290967189198581895e-01,
            0.138326340064778234876692987935644e-01,
            0.174287147234010511276066594996303e-01,
            0.209599884017032127916690979624938e-01,
            0.244133005737814343142984277810598e-01,
            0.277757985941624787538149541869123e-01,
            0.310349712901600079580041445060616e-01,
            0.341786932041883365545669197326863e-01,
            0.371952689232602921339390119057043e-01,
            0.400734762854964539254589560673463e-01,
            0.428026079978800859429404138013489e-01,
            0.453725114076500696293418725266796e-01,
            0.477736262406231013255784824689290e-01,
            0.499970201500574096251975435461280e-01,
            0.520344219366970870569117174684084e-01,
            0.538782523130455619005305302121576e-01,
            0.555216520957386932548485210281212e-01,
            0.569585077202586629708863622371194e-01,
            0.581834739825921408454548343872306e-01,
            0.591919939229615444689604536526858e-01,
            0.599803157775032506093197451947697e-01,
            0.605455069347377959064707614162811e-01,
            0.608854648448563436488434628287051e-01,
            0.609989248412058810561940823432652e-01,
            0.269131695004711131997652715854612e-02, // N = 52
            0.625552396297328019705487777633589e-02,
            0.980263457946275119140613062703602e-02,
            0.133151149823409590897738797839347e-01,
            0.167800233963007367813999099531835e-01,
            0.201848915079807937602648354493117e-01,
            0.235175135539844621531701503520448e-01,
            0.267659537465040120487346677284258e-01,
            0.299185811471439465566437261335624e-01,
            0.329641090897187974012819079259734e-01,
            0.358916348350972328941312788592173e-01,
            0.386906783104239779238914470343838e-01,
            0.413512195005602728093812472667487e-01,
            0.438637342590004079039491622147539e-01,
            0.462192283727847945354635180974535e-01,
            0.484092697440748966957288682228235e-01,
            0.504260185663423769594325319649942e-01,
            0.522622553839069930899678843007186e-01,
            0.539114069327572652031713699402395e-01,
            0.553675696693026530685906238937806e-01,
            0.566255309023685968169272899052640e-01,
            0.576807874525268276441318189886040e-01,
            0.585295617718138686300805570699930e-01,
            0.591688154660429703792904451353524e-01,
            0.595962601712481582735091757073669e-01,
            0.598103657452918602295343491145649e-01,
            0.259168372056703272200955831415407e-02, // N = 53
            0.602427622694867280283238231250656e-02,
            0.944120228494034158938712708463553e-02,
            0.128260261442403778263221225606566e-01,
            0.161667252566874650921471741745227e-01,
            0.194517211076368968489729754054327e-01,
            0.226696730570702116513711460687235e-01,
            0.258094825107575187839045119782342e-01,
            0.288603236178237376225143751781823e-01,
            0.318116784590193213760614954175702e-01,
            0.346533725835342396040094849665233e-01,
            0.373756098034829115928083033151167e-01,
            0.399690058435403832061192815775294e-01,
            0.424246206345200158850154550127607e-01,
            0.447339891036728090604824716621663e-01,
            0.468891503407503118962942304067238e-01,
            0.488826750326991400182463240541013e-01,
            0.507076910692927133141957059889118e-01,
            0.523579072298727199154392189288701e-01,
            0.538276348687310295152354320434724e-01,
            0.551118075239336011323995728851755e-01,
            0.562059983817397095119097061143641e-01,
            0.571064355362671886322510408323139e-01,
            0.578100149917131962183110324249716e-01,
            0.583143113622560116448959849073058e-01,
            0.586175862327202671108003258506728e-01,
            0.587187941511643654251146874641968e-01,
            0.249748183576159174033229250414578e-02, // N = 54
            0.580561101523997898998187389956842e-02,
            0.909936945550939249665989441765559e-02,
            0.123633281288476207073771742590512e-01,
            0.155863030359241252281015371669028e-01,
            0.187575276214693728266093350652919e-01,
            0.218664514228530824267270449654578e-01,
            0.249027414672087669452873673508875e-01,
            0.278563093105958738845344963935976e-01,
            0.307173424978706730214031735441713e-01,
            0.334763364643726455779258613767042e-01,
            0.361241258403835490997185222423605e-01,
            0.386519147821025197536536129323026e-01,
            0.410513061366449719515933795885603e-01,
            0.433143293095970152451018829626652e-01,
            0.454334667282767111151435858654148e-01,
            0.474016788064449912997108953724497e-01,
            0.492124273245288879119465065852781e-01,
            0.508596971461881476344187258377885e-01,
            0.523380161982987442653009355308914e-01,
            0.536424736475536121943655111672685e-01,
            0.547687362130579845719591813081892e-01,
            0.557130625605899867418185455638688e-01,
            0.564723157306259651341720971326238e-01,
            0.570439735587945977016201206419090e-01,
            0.574261370541121144147579487991049e-01,
            0.576175367071470244496417994126978e-01,
            0.240832361997979146639521768878870e-02, // N = 55
            0.559863226656077255816943102418702e-02,
            0.877574610705851573177676319349140e-02,
            0.119251607198486032327262777653945e-01,
            0.150364583335117885752033387782781e-01,
            0.180996145207290501768746396929775e-01,
            0.211048016680164532431464313232941e-01,
            0.240423880097255905802547095681775e-01,
            0.269029614563962939311035660213081e-01,
            0.296773577651610392526907720697430e-01,
            0.323566892261858322750963373089604e-01,
            0.349323728735898906274358063788280e-01,
            0.373961578679655465293709869864708e-01,
            0.397401518743371739235231854052991e-01,
            0.419568463177187671847955697987667e-01,
            0.440391404216066000888231496915833e-01,
            0.459803639462838453005910895640042e-01,
            0.477742985512006686547832826309376e-01,
            0.494151977115517278931105580822351e-01,
            0.508978051244939771111559767815813e-01,
            0.522173715456320886006585411617747e-01,
            0.533696700016054493711746319466697e-01,
            0.543510093299111183055112906523036e-01,
            0.551582460025086723279065816476839e-01,
            0.557887941952841016933499741851860e-01,
            0.562406340710843380656130586963110e-01,
            0.565123182497719976495222310102389e-01,
            0.566029764445604112177721668512012e-01,
            0.232385537577324126890422613947032e-02, // N = 56
            0.540252224601537190925186647397675e-02,
            0.846906316330786565812613486180402e-02,
            0.115098243403834131483340815614335e-01,
            0.145150892780214604537252526538755e-01,
            0.174755129114009174690477507814151e-01,
            0.203819298824025993688444013475539e-01,
            0.232253515625652827068985329293099e-01,
            0.259969870583919714941002634538993e-01,
            0.286882684738227492788897416147350e-01,
            0.312908767473104528455728490533620e-01,
            0.337967671156117592043489475070522e-01,
            0.361981938723152027923247609329598e-01,
            0.384877342592476726158937254941960e-01,
            0.406583113847445313906411627234922e-01,
            0.427032160846670696952367054771230e-01,
            0.446161276526922847501326985102424e-01,
            0.463911333730018899972638644959629e-01,
            0.480227467936002678074540421187404e-01,
            0.495059246830475711251135471112213e-01,
            0.508360826177984848853577260580117e-01,
            0.520091091517414067774472219180510e-01,
            0.530213785240107599265604863619132e-01,
            0.538697618657144802644397889590252e-01,
            0.545516368708894161354131821398505e-01,
            0.550648959017624190201246418808720e-01,
            0.554079525032451250289243250655654e-01,
            0.555797463065143944427894188029340e-01,
            0.224375387225067557012638005784360e-02, // N = 57
            0.521653347471884052265060813845318e-02,
            0.817816006782115894711063950727136e-02,
            0.111157637323359863831239483349987e-01,
            0.140202707907536156415965493265979e-01,
            0.168829590234416248347147395224072e-01,
            0.196952706994885210130458168723211e-01,
            0.224488078907762863256986944263591e-01,
            0.251353509909180704824080353500251e-01,
            0.277468814021801529398075091152708e-01,
            0.302756048426940692700058015788578e-01,
            0.327139743663715516173589213764931e-01,
            0.350547127823125816354042428248872e-01,
            0.372908343244173635879864917577868e-01,
            0.394156654754801443429520359702166e-01,
            0.414228648708011270314718469566759e-01,
            0.433064422162152205049384450393011e-01,
            0.450607761613812054709354847404573e-01,
            0.466806310736415138750306008734841e-01,
            0.481611726616877391156340060514772e-01,
            0.494979824020197497172906853899895e-01,
            0.506870707249274582261317096003564e-01,
            0.517248889205176999915897272338709e-01,
            0.526083397291774430779248438818170e-01,
            0.533347865848192101202083369347245e-01,
            0.539020614832986195888408772706440e-01,
            0.543084714524985734517344522832567e-01,
            0.545528036047618073234425982169500e-01,
            0.546343287565840608635319613666036e-01,
            0.216772324962752860609722283766349e-02, // N = 58
            0.503998161265050099473450878388375e-02,
            0.790197384999850553149676803933495e-02,
            0.107415535328787474579077565721800e-01,
            0.135502371129887348351430897439451e-01,
            0.163198742349710699284450347325559e-01,
            0.190424654618931506292476719739623e-01,
            0.217101561401465815234238669570227e-01,
            0.243152527249638252167325188580498e-01,
            0.268502431819820872689164071701450e-01,
            0.293078180441603473017116478087213e-01,
            0.316808912538093047973485637749997e-01,
            0.339626204934159321760220110314534e-01,
            0.361464268670872760245627576015715e-01,
            0.382260138458584118636328904280765e-01,
            0.401953854098679026731470834636520e-01,
            0.420488633295820913174656364948234e-01,
            0.437811035336402714104862527700808e-01,
            0.453871115148197013301040963200673e-01,
            0.468622567290264945157696788052520e-01,
            0.482022859454177809542925373509146e-01,
            0.494033355089624557067845430582524e-01,
            0.504619424799530741344865615837751e-01,
            0.513750546182856833183799961824903e-01,
            0.521400391836697741376828050049180e-01,
            0.527546905263707994798962177284939e-01,
            0.532172364465790117672575114630977e-01,
            0.535263433040582752149865301145692e-01,
            0.536811198633348445099834560135582e-01,
            0.209549228454115085910348399866448e-02, // N = 59
            0.487223916826538608120757620104404e-02,
            0.763952945348786139675181360500841e-02,
            0.103858855009953235440093874014652e-01,
            0.131033663063442503276163214635613e-01,
            0.157843473130815538403682535616050e-01,
            0.184213427536098577567207525118749e-01,
            0.210069982884367477059953925965200e-01,
            0.235341053937141003165019887794142e-01,
            0.259956197312984286578107581680860e-01,
            0.283846802005354566338975069559749e-01,
            0.306946278361112857642675133871340e-01,
            0.329190242710452996686427782673800e-01,
            0.350516696363997411414557323131216e-01,
            0.370866198188711290155334282894867e-01,
            0.390182030161600317914459046555289e-01,
            0.408410355386869957112091216936823e-01,
            0.425500368110670563987661617606025e-01,
            0.441404435302978459585950547736296e-01,
            0.456078229405092534443324554315076e-01,
            0.469480851869628827201274335221608e-01,
            0.481574947146065147241339086576990e-01,
            0.492326806793616163320533984885165e-01,
            0.501706463429962847475966730214137e-01,
            0.509687774253940443177758031824192e-01,
            0.516248493908914535720594792308901e-01,
            0.521370336483759811944129010135149e-01,
            0.525039026478278622063791750028691e-01,
            0.527244338591281351836211334223332e-01,
            0.527980126219896053956592277024162e-01,
            0.202681196887342690388996289808517e-02, // N = 60
            0.471272992695368602305977645798224e-02,
            0.738993116334445829099336220995854e-02,
            0.100475571822885548645559198461963e-01,
            0.126781664768167038571573234696971e-01,
            0.152746185967848027990793321778172e-01,
            0.178299010142079887259503726334636e-01,
            0.203371207294555471512356476061821e-01,
            0.227895169440000734360714743015603e-01,
            0.251804776215188925494546714794599e-01,
            0.275035567499246495975154466014310e-01,
            0.297524915007880415327130663973476e-01,
            0.319212190192974929570620322653765e-01,
            0.340038927249452944002641733996239e-01,
            0.359948980510843516295557518336952e-01,
            0.378888675692434812500509599695607e-01,
            0.396806954523812685521295275707026e-01,
            0.413655512355844458757874658762941e-01,
            0.429388928359368111921249147914843e-01,
            0.443964787957866109942779548140014e-01,
            0.457343797161145778119773166609880e-01,
            0.469489888489119652420074834392926e-01,
            0.480370318199719788776383177148973e-01,
            0.489955754557561750043496864560604e-01,
            0.498220356905505025784307543078473e-01,
            0.505141845325088140823421352653166e-01,
            0.510701560698555711966604404473462e-01,
            0.514884515009809615603083630970976e-01,
            0.517679431749101672484980162649567e-01,
            0.519078776312206306926327501092321e-01,
            0.196145336166974360252310730973366e-02, // N = 61
            0.456092400601278977476786109285585e-02,
            0.715235499174801172822093992571763e-02,
            0.972546183036006935395768780170789e-02,
            0.122732635078106540710815130025685e-01,
            0.147890658849421405025292203445132e-01,
            0.172662929876068128853637188300865e-01,
            0.196984777461065476769524151450002e-01,
            0.220792731483141231707145991891915e-01,
            0.244024671875490021487321528492655e-01,
            0.266619985241463410358300646035491e-01,
            0.288519720881873295896585861891525e-01,
            0.309666743683954278525139227970176e-01,
            0.330005882759102580974288931385501e-01,
            0.349484075165312256369976536900406e-01,
            0.368050504231597384343067782085192e-01,
            0.385656732070035003411116743299607e-01,
            0.402256825910009823395851326518323e-01,
            0.417807477908831702713725738043242e-01,
            0.432268118124981974387355798422097e-01,
            0.445601020350801873493761666352158e-01,
            0.457771400531469812900921756470556e-01,
            0.468747507508036829804464696522911e-01,
            0.478500705851001798415218786277589e-01,
            0.487005550564075133439415118120847e-01,
            0.494239853467433845759663731177030e-01,
            0.500184741081758475637498109182848e-01,
            0.504824703868021063730634389280763e-01,
            0.508147636688145133850277829847859e-01,
            0.510144870386962414093945916878333e-01,
            0.510811194407819869756124378422272e-01
        };

        public static readonly double[] KronrodPoint =
        {
            7.74596669241483404277914814883843e-01, // N = 3
            0.0e+00,
            9.25820099772551419192723187734373e-01, // N = 5
            5.77350269189625620036565578629961e-01,
            0.0e+00,
            9.60491268708020373701117478049127e-01, // N = 7
            7.74596669241483404277914814883843e-01,
            4.34243749346802210276052846893435e-01,
            0.0e+00,
            9.76560250737573021240223170025274e-01, // N = 9
            8.61136311594052239470897802675609e-01,
            6.40286217496309761898487522557843e-01,
            3.39981043584856257311344052141067e-01,
            0.0e+00,
            9.84085360094842709344220565981232e-01, // N = 11
            9.06179845938664407789531196613098e-01,
            7.54166726570849044186672927025938e-01,
            5.38469310105682996692166852881201e-01,
            2.79630413161783220044043218877050e-01,
            0.0e+00,
            9.88703202612678411220770158251980e-01, // N = 13
            9.32469514203151716991158082237234e-01,
            8.21373340865027889989846698881593e-01,
            6.61209386466264592563391033763764e-01,
            4.63118212475304602548931143246591e-01,
            2.38619186083196987979704317694996e-01,
            0.0e+00,
            9.91455371120812833929392127174651e-01, // N = 15
            9.49107912342758597290526267897803e-01,
            8.64864423359769096677496236225124e-01,
            7.41531185599394460083999547350686e-01,
            5.86087235467691591850325494306162e-01,
            4.05845151377397406200486784655368e-01,
            2.07784955007898564094404036950436e-01,
            0.0e+00,
            9.93379875881715834751162219617981e-01, // N = 17
            9.60289856497536065127462734380970e-01,
            8.94120906847456264898710287525319e-01,
            7.96666477413626505921229181694798e-01,
            6.72354070945158865946211790287634e-01,
            5.25532409916329323884554014512105e-01,
            3.60701097928131819703168048363295e-01,
            1.83434642495649724569517502459348e-01,
            0.0e+00,
            9.94678160677340272854962677229196e-01, // N = 19
            9.68160239507626529942285742436070e-01,
            9.14963507249678009713989013107494e-01,
            8.36031107326635880561127578403102e-01,
            7.34486765183933520972914266167209e-01,
            6.13371432700590468733992111083353e-01,
            4.75462479112459812657931479407125e-01,
            3.24253423403808638258993823910714e-01,
            1.64223563614986717285049167003308e-01,
            0.0e+00,
            9.95657163025807867562377850845223e-01, // N = 21
            9.73906528517171743430935748619959e-01,
            9.30157491355708354596742992725922e-01,
            8.65063366688984314301080758013995e-01,
            7.80817726586416904765997060167138e-01,
            6.79409568299024102522309931373456e-01,
            5.62757134668604330762775589391822e-01,
            4.33395394129247379932934336466133e-01,
            2.94392862701460422680810324891354e-01,
            1.48874338981631160194751828385051e-01,
            0.0e+00,
            9.96369613889542482532135636574822e-01, // N = 23
            9.78228658146056861966144424513914e-01,
            9.41677108578067856292648230009945e-01,
            8.87062599768095094709963177592726e-01,
            8.16057456656220758794972880423302e-01,
            7.30152005574049245417711517802672e-01,
            6.30599520161965076958665576967178e-01,
            5.19096129206812140211013684165664e-01,
            3.97944140952377511943893750867574e-01,
            2.69543155952345125925262436794583e-01,
            1.36113000799362088288901873056602e-01,
            0.0e+00,
            9.96933922529595228922971728025004e-01, // N = 25
            9.81560634246719354578658567334060e-01,
            9.50537795943121377462148302583955e-01,
            9.04117256370474686733018643280957e-01,
            8.43558124161153055631245933909668e-01,
            7.69902674194304470489669256494381e-01,
            6.84059895470055967514610983926104e-01,
            5.87317954286617260883929247938795e-01,
            4.81339450478157293566994212596910e-01,
            3.67831498998180128623403106757905e-01,
            2.48505748320469427303791576377989e-01,
            1.25233408511468857771120610777871e-01,
            0.0e+00,
            9.97366176994825104351605205010856e-01, // N = 27
            9.84183054718588357090425233764108e-01,
            9.57552468386081434559287117735948e-01,
            9.17598399222978255984628503938438e-01,
            8.65333160266344436628571656910935e-01,
            8.01578090733309878146428673062474e-01,
            7.26948849320632306536538180807838e-01,
            6.42349339440340227902481728960993e-01,
            5.49079957956536968133320897322847e-01,
            4.48492751036446757328945977860712e-01,
            3.41832463021806476355379800224910e-01,
            2.30458315955134912522694889958075e-01,
            1.15971089744933600340637269709987e-01,
            0.0e+00,
            9.97720593756543205898879023152404e-01, // N = 29
            9.86283808696812314131818766327342e-01,
            9.63158338278853110026034300972242e-01,
            9.28434883663573629064558190293610e-01,
            8.82914663252057252407212217804044e-01,
            8.27201315069764908649574408627814e-01,
            7.61756752562205652345994622010039e-01,
            6.87292904811685367860718542942777e-01,
            6.04789365940921808117991531617008e-01,
            5.15248636358153988545893753325799e-01,
            4.19655897642978947814640378055628e-01,
            3.19112368927889633596350904554129e-01,
            2.14835918533484881987050130192074e-01,
            1.08054948707343417835247123548470e-01,
            0.0e+00,
            9.98002298693397182915987286833115e-01, // N = 31
            9.87992518020485377405748295132071e-01,
            9.67739075679138860408556865877472e-01,
            9.37273392400705951388317771488801e-01,
            8.97264532344082099690751874732086e-01,
            8.48206583410427428226796564558754e-01,
            7.90418501442466170381351275864290e-01,
            7.24417731360170069621062793885358e-01,
            6.50996741297416692262345350172836e-01,
            5.70972172608538719451587439834839e-01,
            4.85081863640239585588886939149234e-01,
            3.94151347077563662946175782053615e-01,
            2.99180007153169003064618891585269e-01,
            2.01194093997434320097994486786774e-01,
            1.01142066918717341006406229553249e-01,
            0.0e+00,
            9.98239274145444333008470039203530e-01, // N = 33
            9.89400934991649716465644814888947e-01,
            9.71505950969392517713174584059743e-01,
            9.44575023073232156178846707916819e-01,
            9.09157667012342796120094590150984e-01,
            8.65631202387831533151540952530922e-01,
            8.14240287062444223487034378194949e-01,
            7.55404408355002887631712837901432e-01,
            6.89741106681762028429716337996069e-01,
            6.17876244402643437503286349965492e-01,
            5.40407676352139598741075587895466e-01,
            4.58016777657227425191166503282147e-01,
            3.71483780878416325332835867811809e-01,
            2.81603550779259248493247014266672e-01,
            1.89168579018083871101651993740234e-01,
            9.50125098376376625575190359995759e-02,
            0.0e+00,
            9.98432970606058178830721772101242e-01, // N = 35
            9.90575475314417253080989667068934e-01,
            9.74659256967431053553241326881107e-01,
            9.50675521768767683994383332901634e-01,
            9.19096136803891461397597595350817e-01,
            8.80239153726985912307156922906870e-01,
            8.34274092850134429966146853985265e-01,
            7.81514003896801145998551874072291e-01,
            7.22472287372409871508693868236151e-01,
            6.57671159216690837112651024654042e-01,
            5.87569212334035029243750614114106e-01,
            5.12690537086476605388440930255456e-01,
            4.33687295209799150708107617901987e-01,
            3.51231763453875855951480389194330e-01,
            2.65946507451681912748142622149317e-01,
            1.78484181495847438192470235662768e-01,
            8.95856394252265292310610789172642e-02,
            0.0e+00,
            9.98599165412682676645772517076693e-01, // N = 37
            9.91565168420931009052310400875285e-01,
            9.77310380774861098274186588241719e-01,
            9.55823949571397601943090194254182e-01,
            9.27504501573343409503991097153630e-01,
            8.92602466497555813162989579723217e-01,
            8.51249373433717426706834885408171e-01,
            8.03704958972523364479911833768710e-01,
            7.50380481703357804512677375896601e-01,
            6.91687043060353334844592154695420e-01,
            6.28003754863833640875725450314349e-01,
            5.59770831073947316980365940253250e-01,
            4.87509042585078489207006668948452e-01,
            4.11751161462842685256902086621267e-01,
            3.33023422791407619492076719325269e-01,
            2.51886225691505316603979736100882e-01,
            1.68936828066548888616082990665745e-01,
            8.47750130417350422629141348807025e-02,
            0.0e+00,
            9.98738012080314652152424059750047e-01, // N = 39
            9.92406843843584351994024927989813e-01,
            9.79572300789263605835799353371840e-01,
            9.60208152134830017487843178969342e-01,
            9.34664000165519315288520374451764e-01,
            9.03155903614818122981944270577515e-01,
            8.65773542685335240065569450962357e-01,
            8.22714656537143040893056422646623e-01,
            7.74328859009534631319127129245317e-01,
            7.20966177335228941558398219058290e-01,
            6.62923065744907780150185772072291e-01,
            6.00545304661680989788408169260947e-01,
            5.34275632530553434840214777068468e-01,
            4.64570741375960827301838662606315e-01,
            3.91851230871520184173562029172899e-01,
            3.16564099963629608236459489489789e-01,
            2.39224928318241325531090524236788e-01,
            1.60358645640225422335234384263458e-01,
            8.04519227440115697325140331486182e-02,
            0.0e+00,
            9.98859031588277712643275663140230e-01, // N = 41
            9.93128599185094884660429670475423e-01,
            9.81507877450250143525067869632039e-01,
            9.63971927277913365195161077281227e-01,
            9.40822633831754462363505808752961e-01,
            9.12234428251325946135352751298342e-01,
            8.78276811252282185726869556674501e-01,
            8.39116971822218782328661745850695e-01,
            7.95041428837550689934232650557533e-01,
            7.46331906460150462656599756883224e-01,
            6.93237656334751317643849688465707e-01,
            6.36053680726514802934445924620377e-01,
            5.75140446819710104975342801481020e-01,
            5.10867001950827015477329950954299e-01,
            4.43593175238724879427820724231424e-01,
            3.73706088715419659784799932822352e-01,
            3.01627868114912933705795694550034e-01,
            2.27785851141645345752095863645081e-01,
            1.52605465240922860692407425631245e-01,
            7.65265211334970607559569089062279e-02,
            0.0e+00,
            9.98961930687316979060597077477723e-01, // N = 43
            9.93752170620389452260212692635832e-01,
            9.83184863561686106514514449372655e-01,
            9.67226838566306312827691726852208e-01,
            9.46147216778512656354394039226463e-01,
            9.20099334150401015897102752205683e-01,
            8.89128315331184304604050794296199e-01,
            8.53363364583317296485631686664419e-01,
            8.13052580847531847219045175734209e-01,
            7.68439963475677778603767364984378e-01,
            7.19723452572024857687438270659186e-01,
            6.67138804197412560448299245763337e-01,
            6.10997123789766005685919481038582e-01,
            5.51618835887220049229995311179664e-01,
            4.89295908895668762994546341360547e-01,
            4.24342120207438944223810040057288e-01,
            3.57125253659921149118616767736967e-01,
            2.88021316802401172729730660648784e-01,
            2.17380093871728852228386585920816e-01,
            1.45561854160894815768401144850941e-01,
            7.29672475957908045485211800951220e-02,
            0.0e+00,
            9.99052772392180266081140871392563e-01, // N = 45
            9.94294585482399351228366413124604e-01,
            9.84640721597348722582410118775442e-01,
            9.70060497835428914292776880756719e-01,
            9.50790380343184859945893094845815e-01,
            9.26956772187173649868441316357348e-01,
            8.98593852179612295749677741696360e-01,
            8.65812577720300069472614268306643e-01,
            8.28820204471430677095611372351414e-01,
            7.87816805979208112375999917276204e-01,
            7.42971193879007452132157141022617e-01,
            6.94487263186682857174503169517266e-01,
            6.42622572592912555400346263922984e-01,
            5.87640403506911712661064939311473e-01,
            5.29793398630515000036211858969182e-01,
            4.69355837986757229440826222344185e-01,
            4.06633105434211661322052577816066e-01,
            3.41935820892083852662324261473259e-01,
            2.75571451345615225925200775236590e-01,
            2.07860426688221355817631774698384e-01,
            1.39137790722961979250626995963103e-01,
            6.97392733197221420526901169978373e-02,
            0.0e+00,
            9.99131136463421554161357107659569e-01, // N = 47
            9.94769334997552157062727928860113e-01,
            9.85918150727375652841999453812605e-01,
            9.72542471218115212039379002817441e-01,
            9.54855839860111244021823040384334e-01,
            9.32971086826015816306778560829116e-01,
            9.06907694741281411587863203749293e-01,
            8.76752358270442067045280509773875e-01,
            8.42687322997013099623586640518624e-01,
            8.04888401618840232387697142257821e-01,
            7.63491316221165616795474306854885e-01,
            7.18661363131950281513127265498042e-01,
            6.70623789037042561389512229652610e-01,
            6.19609875763646456015010244300356e-01,
            5.65827305907601885159863286389736e-01,
            5.09501477846007522209959006431745e-01,
            4.50900980924738292721087873360375e-01,
            3.90301038030290592395488147303695e-01,
            3.27957345711785142050587182893651e-01,
            2.64135680970345232410068092576694e-01,
            1.99134670993493134716345593915321e-01,
            1.33256824298466497458193202874099e-01,
            6.67836574066257848691918752592755e-02,
            0.0e+00,
            9.99201056021875144708133120730054e-01, // N = 49
            9.95187219997021421669103347085183e-01,
            9.87040496015809343255398289329605e-01,
            9.74728555971309362782051266549388e-01,
            9.58441684405209493036181811476126e-01,
            9.38274552002732797895134808641160e-01,
            9.14240690794911659011745541647542e-01,
            8.86415527004400738420031302666757e-01,
            8.54953803904051512496664599893847e-01,
            8.20001985973903169124810119683389e-01,
            7.81677226476464204196759055776056e-01,
            7.40124191578554357917596462357324e-01,
            6.95532072396779055267757030378561e-01,
            6.48093651936975545524433073296677e-01,
            5.97990513906078269279475989605999e-01,
            5.45421471388839562699502039322397e-01,
            4.90612365463446109536960193509003e-01,
            4.33793507626045515834789512155112e-01,
            3.75191154797950676691442595256376e-01,
            3.15042679696163507863104769057827e-01,
            2.53600430369677443120934867692995e-01,
            1.91118867473616310670436746477208e-01,
            1.27851240286216916164363510688418e-01,
            6.40568928626057132458271325958776e-02,
            0.0e+00,
            9.99262104992609589970697925309651e-01, // N = 51
            9.95556969790497903183279504446546e-01,
            9.88035794534077194128940391237848e-01,
            9.76663921459517081480328215548070e-01,
            9.61614986425842532824503905430902e-01,
            9.42974571228974323133797952323221e-01,
            9.20747115281701833389149669528706e-01,
            8.94991997878275102884515490586637e-01,
            8.65847065293275375275072747172089e-01,
            8.33442628760833748025049771968042e-01,
            7.97873797998499667549765490548452e-01,
            7.59259263037357023939932787470752e-01,
            7.17766406813084456572937597229611e-01,
            6.73566368473468291000472163432278e-01,
            6.26810099010317145484805223532021e-01,
            5.77662930241222949412360776477726e-01,
            5.26325284334718701551025787921390e-01,
            4.73002731445714641456135041153175e-01,
            4.17885382193037779874345005737268e-01,
            3.61172305809387805819454797529033e-01,
            3.03089538931108182229223757531145e-01,
            2.43866883720988331107903945849102e-01,
            1.83718939421049054505630238054437e-01,
            1.22864692610710410369811995678901e-01,
            6.15444830056854352839934563235147e-02,
            0.0e+00,
            9.99317064760071649409667315921979e-01, // N = 53
            9.95885701145616808460658830881584e-01,
            9.88919144824434881435593069909373e-01,
            9.78385445956470922723724470415618e-01,
            9.64441118239312333848545222281246e-01,
            9.47159066661714454937737173167989e-01,
            9.26540570770361004981907626643078e-01,
            9.02637861984306844043146611511474e-01,
            8.75569635163670922928247364325216e-01,
            8.45445942788498161490906568360515e-01,
            8.12349727085128203718511485931231e-01,
            7.76385948820678795101457581040449e-01,
            7.37696979507612815574191245104885e-01,
            6.96427260419957061543527743197046e-01,
            6.52710009506913380050718842539936e-01,
            6.06692293017617845229949580243556e-01,
            5.58544530980815689957807990140282e-01,
            5.08440714824505701763257548009278e-01,
            4.56550216028299815640423275908688e-01,
            4.03051755123486177279090725278365e-01,
            3.48138197103694813083762937822030e-01,
            2.92004839485956679823175363708287e-01,
            2.34845255152457549341349363203335e-01,
            1.76858820356889961944446554298338e-01,
            1.18251662892057157749903240073763e-01,
            5.92300934293130201813148971723422e-02,
            0.0e+00,
            9.99365546522977044041624594683526e-01, // N = 55
            9.96179262888988503732434764970094e-01,
            9.89709602301697688453430146182654e-01,
            9.79923475961500756170607928652316e-01,
            9.66964925626242921552488951419946e-01,
            9.50900557814704727732646460935939e-01,
            9.31725922454987864895770144357812e-01,
            9.09482320677491240523693249997450e-01,
            8.84276659710189316676576254394604e-01,
            8.56207908018294383545310211047763e-01,
            8.25343907246362085139423925284063e-01,
            7.91771639070507959878852943802485e-01,
            7.55618350427228357979458905901993e-01,
            7.17013473739423923269953320414061e-01,
            6.76068826884504314733703722595237e-01,
            6.32907971946495173654056998202577e-01,
            5.87683411872107930307151946180966e-01,
            5.40551564579456522707801013893913e-01,
            4.91656061412170497515461420334759e-01,
            4.41148251750026643147606364436797e-01,
            3.89201852747204479765485984898987e-01,
            3.35993903638508506492854621683364e-01,
            2.81689781320006937814781622364535e-01,
            2.26459365439536680630894238674955e-01,
            1.70490430850875285262446823253413e-01,
            1.13972585609529830641406533686677e-01,
            5.70829167231878126242961002390075e-02,
            0.0e+00,
            9.99409527464458324885754336719401e-01, // N = 57
            9.96442497573954089062908678897657e-01,
            9.90417243607036867913961941667367e-01,
            9.81303165370872920725275889708428e-01,
            9.69231347359594486157163828465855e-01,
            9.54259280628938277857287175720558e-01,
            9.36380950324850358512662751309108e-01,
            9.15633026392132176596305725979619e-01,
            8.92108688876811939394428918603808e-01,
            8.65892522574395195888996568100993e-01,
            8.37044208419339241800116724334657e-01,
            8.05641370917179133748220465349732e-01,
            7.71793447243434016513674578163773e-01,
            7.35610878013631563909768829034874e-01,
            6.97193171944897938097085443587275e-01,
            6.56651094038864902024954517401056e-01,
            6.14115617729884100128856516676024e-01,
            5.69720471811401840689370601467090e-01,
            5.23594465442833056911808853328694e-01,
            4.75874224955118385604890818285639e-01,
            4.26709291931107070894313437747769e-01,
            3.76251516089078807958401284849970e-01,
            3.24650637057820157238552383205388e-01,
            2.72061627635178326922726910197525e-01,
            2.18646765777540580399929126542702e-01,
            1.64569282133380900834396243226365e-01,
            1.09991649290732920740687461602647e-01,
            5.50792898840343839172994933051086e-02,
            0.0e+00,
            9.99448667882050778565883319970453e-01, // N = 59
            9.96679442260596570868358412553789e-01,
            9.91055405722805371482309055863880e-01,
            9.82545505261413265607473022100748e-01,
            9.71271237101307027828056561702397e-01,
            9.57285595778087805562961420946522e-01,
            9.40578916002972831300610323523870e-01,
            9.21180232953058952816149940190371e-01,
            8.99174270592779323330034912942210e-01,
            8.74637804920102679417936997197103e-01,
            8.47619919760977058587059218552895e-01,
            8.18185487615252449167257964290911e-01,
            7.86433199580495512215350117912749e-01,
            7.52462851734477466969508441252401e-01,
            7.16358665327582411208595658536069e-01,
            6.78214537602686351469571945926873e-01,
            6.38148568478847155738264973479090e-01,
            5.96281797138227931398546388663817e-01,
            5.52724357701319446434240489907097e-01,
            5.07592955124228195629143556288909e-01,
            4.61023045388234409269756497451453e-01,
            4.13152888174009136346143122864305e-01,
            3.64111378713378119886812100958196e-01,
            3.14031637867639989991630500298925e-01,
            2.63061896295217478858319282153388e-01,
            2.11352286166000963296696113502549e-01,
            1.59043478004521871005394473286287e-01,
            1.06278230132678980224270048893231e-01,
            5.32117722046491353760089282332046e-02,
            0.0e+00,
            9.99484410050490490462493653467391e-01, // N = 61
            9.96893484074649172121951323788380e-01,
            9.91630996870404346488214741839329e-01,
            9.83668123279747175224940747284563e-01,
            9.73116322501125785571218784753000e-01,
            9.60021864968307214738274524279404e-01,
            9.44374444748559804807541695481632e-01,
            9.26200047429274420096589892636985e-01,
            9.05573307699907403822692231187830e-01,
            8.82560535792052069936630687152501e-01,
            8.57205233546060485494422209740151e-01,
            8.29565762382768023819323843781604e-01,
            7.99727835821838928254123857186642e-01,
            7.67777432104825741099318747728830e-01,
            7.33790062453226643590653566207038e-01,
            6.97850494793315401231836858642055e-01,
            6.60061064126626795278696135937935e-01,
            6.20526182989242558463161003601272e-01,
            5.79345235826361437680986909981584e-01,
            5.36624148142019863350071773311356e-01,
            4.92480467861778292704144632807584e-01,
            4.47033769538089376105460814869730e-01,
            4.00401254830394681683003454963909e-01,
            3.52704725530878282491187292180257e-01,
            3.04073202273625220470876229228452e-01,
            2.54636926167890076388999887058162e-01,
            2.04525116682310353910523303966329e-01,
            1.53869913608583541719809772985172e-01,
            1.02806937966737399481331749484525e-01,
            5.14718425553176983644476649715216e-02,
            0.0e+00,
            9.99516462879228351212645975465421e-01, // N = 63
            9.97087481819476706412785915745189e-01,
            9.92153590932694062765051512542414e-01,
            9.84685909665152570013901822676416e-01,
            9.74788362516032513838126760674641e-01,
            9.62503925092949463859781644714531e-01,
            9.47819958262127615356007481750567e-01,
            9.30756997896648008428144294157391e-01,
            9.11383461987592791153645066515310e-01,
            8.89760029948270747546246184356278e-01,
            8.65922609043559332597794764296850e-01,
            8.39920320146267163075037842645543e-01,
            8.11831075102920074471057887421921e-01,
            7.81733148416624890053583385451930e-01,
            7.49690911026608564071693763253279e-01,
            7.15776784586852898861764060711721e-01,
            6.80083687850750795433896200847812e-01,
            6.42706722924260454021805344382301e-01,
            6.03731488500522717188800925214309e-01,
            5.63249161407149201430399898526957e-01,
            5.21366801919327049752439506846713e-01,
            4.78193782044902537808894749105093e-01,
            4.33831684206103185275082978478167e-01,
            3.88385901608232997350711457329453e-01,
            3.41974685364181518743009746685857e-01,
            2.94718069981701968895748677823576e-01,
            2.46728632359113658756299969354586e-01,
            1.98121199335570846722376359139162e-01,
            1.49021273651722158115617844487133e-01,
            9.95553121523416878480006175777817e-02,
            4.98418078330689212629422968348081e-02,
            0.0e+00,
            9.99545902124364449292670542490669e-01, // N = 65
            9.97263861849481458854427273763577e-01,
            9.92628035262972052699126379593508e-01,
            9.85611511545268492717752906173700e-01,
            9.76310283614663876328165770246414e-01,
            9.64762255587506500909000806132099e-01,
            9.50954684848661191409746606950648e-01,
            9.34906075937739555747896247339668e-01,
            9.16677266651364286431658001674805e-01,
            8.96321155766052202196192411065567e-01,
            8.73869768945310432251005750003969e-01,
            8.49367613732569970430574812780833e-01,
            8.22882950136051283251958921027835e-01,
            7.94483795967942385551907591434428e-01,
            7.64228251997803864625780079222750e-01,
            7.32182118740290044378582479112083e-01,
            6.98426557795210345425118703133194e-01,
            6.63044266930215564492812063690508e-01,
            6.26112937701823968339454040687997e-01,
            5.87715757240762415314350164408097e-01,
            5.47946314199152628710010048962431e-01,
            5.06899908932229359415089220419759e-01,
            4.64669308481992060499976560095092e-01,
            4.21351276130635277183955622604117e-01,
            3.77049421154121044974516507863882e-01,
            3.31868602282127833635883007445955e-01,
            2.85912458589459961277867705575773e-01,
            2.39287362252137536522411664918764e-01,
            1.92103608983142881694305970086134e-01,
            1.44471961582796709633313980702951e-01,
            9.65026968768942505771946116510662e-02,
            4.83076656877380675170208235158498e-02,
            0.0e+00,
            9.99572480401970664409816436091205e-01, // N = 67
            9.97424694246454968116211148299044e-01,
            9.93061355532605327667283745540772e-01,
            9.86455726230642260254910524963634e-01,
            9.77697766395559941798865111195482e-01,
            9.66822909689992404658198665856617e-01,
            9.53816931548339130841895894263871e-01,
            9.38694372611168059705732957809232e-01,
            9.21511400117664969400266272714362e-01,
            9.02316767743433501003380570182344e-01,
            8.81136957366152051562835367803928e-01,
            8.58009652676503753454539946687873e-01,
            8.32997339086677390795898645592388e-01,
            8.06162356274166214120668882969767e-01,
            7.77554541237250207430520276830066e-01,
            7.47230496449561631955305074370699e-01,
            7.15264381722218511860944545333041e-01,
            6.81731959969742673521864162466954e-01,
            6.46700582975177629130314471694874e-01,
            6.10242345836378707879532612423645e-01,
            5.72442931691055756360242412483785e-01,
            5.33389904786347623932840633642627e-01,
            4.93164173270868089193896821598173e-01,
            4.51850017272450443783782247919589e-01,
            4.09542745071417801927537993833539e-01,
            3.66339257748072966158758845267585e-01,
            3.22330369697089780256504809585749e-01,
            2.77609097152497152904970789677463e-01,
            2.32277655397241128421015332605748e-01,
            1.86439298827991373208590175636346e-01,
            1.40191060341774725861441197594104e-01,
            9.36310658547330892931270795997989e-02,
            4.68652733813287036834793752859696e-02,
            0.0e+00,
            9.99597015785066211890352860791609e-01, // N = 69
            9.97571753790841619924378846917534e-01,
            9.93457022641509590599184775783215e-01,
            9.87227816406309521823914110427722e-01,
            9.78967718582760548784449383674655e-01,
            9.68708262533344299782811503973790e-01,
            9.56435429333021058795338831259869e-01,
            9.42162397405107210346386636956595e-01,
            9.25939527470533874087266212882241e-01,
            9.07809677718324659068116488924716e-01,
            8.87796593664716304772355215391144e-01,
            8.65934638334564410477867113513639e-01,
            8.42278986723549505377661716920557e-01,
            8.16884227900933623800483474042267e-01,
            7.89795615219529123507413714833092e-01,
            7.61064876629872655300346195872407e-01,
            7.30757257014758798696618669055169e-01,
            6.98939113216263341321621282986598e-01,
            6.65671902786864166934321929147700e-01,
            6.31021727080528394004943493200699e-01,
            5.95063987759908319397084142110543e-01,
            5.57875500669746671178472752217203e-01,
            5.19530467383866101371836521138903e-01,
            4.80106545190326861050067464020685e-01,
            4.39687752436393519683832664668444e-01,
            3.98359277758645713429785928383353e-01,
            3.56204949553047378607573136832798e-01,
            3.13311081339463060047023645893205e-01,
            2.69768000950774633484030573526979e-01,
            2.25666691616449310853198539916775e-01,
            1.81097495284798515324808931836742e-01,
            1.36152357259183010018688264608500e-01,
            9.09251724409930600634410780003236e-02,
            4.55098219531021030981321473518619e-02,
            0.0e+00,
            9.99619298560587732360716017865343e-01, // N = 71
            9.97706569099600315553288965020329e-01,
            9.93820293038909063909613905707374e-01,
            9.87935764443851338612034851394128e-01,
            9.80131657851340709619591962109553e-01,
            9.70437616039229955511302705417620e-01,
            9.58838696995843009496240938460687e-01,
            9.45345148207827001840541925048456e-01,
            9.30003753050705816995957775361603e-01,
            9.12854261359317131763191355275922e-01,
            8.93916305839049241122040712070884e-01,
            8.73219125025222031588612026098417e-01,
            8.50813544681091160626351665996481e-01,
            8.26749899092225182251070236816304e-01,
            8.01067213125705612775107056222623e-01,
            7.73810252286912580999000965675805e-01,
            7.45038975666406422249110619304702e-01,
            7.14814501556628623113454068516148e-01,
            6.83190418488156314680281866458245e-01,
            6.50224364665890064429731864947826e-01,
            6.15985710487221616027397885773098e-01,
            5.80545344749764269387526383070508e-01,
            5.43968351696258012317741759034107e-01,
            5.06322773241488444107005761907203e-01,
            4.67686183461529514371335380928940e-01,
            4.28137541517814079750081646125182e-01,
            3.87750696027842511881544851348735e-01,
            3.46601554430814084994949553220067e-01,
            3.04774001471050381972816012421390e-01,
            2.62352941209295809077417516164132e-01,
            2.19418258415018024853893052750209e-01,
            1.76051061165989675139087466959609e-01,
            1.32339270613416964961217558993667e-01,
            8.83713432756591671379808872188732e-02,
            4.42304079604761840593951660594030e-02,
            0.0e+00,
            9.99639961514879438198022398864850e-01, // N = 73
            9.97830462484085689567336885374971e-01,
            9.94153696684936805105792245740304e-01,
            9.88586478902212184571851594228065e-01,
            9.81202279982642422417882244189968e-01,
            9.72027691049697772918136706721270e-01,
            9.61048148322967143997175298864022e-01,
            9.48272984399507579134080970106879e-01,
            9.33744457633886137948309169587446e-01,
            9.17497774515658837124476576718735e-01,
            8.99550617190168932957305969466688e-01,
            8.79929800890397073587223530921619e-01,
            8.58680523229590431100177738699131e-01,
            8.35847166992474965852011337119620e-01,
            8.11465360006536462478266003017779e-01,
            7.85576230132206565492936078953790e-01,
            7.58232874152525937461177818477154e-01,
            7.29489171593556751105325020034797e-01,
            6.99394262480945050342029389867093e-01,
            6.68001236585521018795930103806313e-01,
            6.35371511784057152461002715426730e-01,
            6.01567658135980787292851346137468e-01,
            5.66649609403106824245810457796324e-01,
            5.30680285926245498551168111589504e-01,
            4.93728458077752119237402439466678e-01,
            4.55863944433420709145821092533879e-01,
            4.17155110553159791386690358194755e-01,
            3.77672547119689006045462065230822e-01,
            3.37490767013667758433825838437770e-01,
            2.96684995344028201724739801647956e-01,
            2.55329699932149156715865956357447e-01,
            2.13500892316865448217200196268095e-01,
            1.71276852197153162116194380359957e-01,
            1.28736103809384605511922927689739e-01,
            8.59568500443915195496913383976789e-02,
            4.30181984737084827097319816857635e-02,
            0.0e+00,
            9.99658826759632690439616453659255e-01, // N = 75
            9.97944582477913177953610102122184e-01,
            9.94461234288736228847938036778942e-01,
            9.89185963214318619840526025654981e-01,
            9.82188189256598565002320810890524e-01,
            9.73493030056485353362916157493601e-01,
            9.63085370067332302568274826626293e-01,
            9.50972343262094566007647244987311e-01,
            9.37193420230154727867954989051213e-01,
            9.21781437412463544589513730898034e-01,
            9.04750981775800378059670947550330e-01,
            8.86124962155485973447355263488134e-01,
            8.65945248518772414669797399255913e-01,
            8.44252987340555760553684194746893e-01,
            8.21079044176752592676393760484643e-01,
            7.96459200509902154330177381780231e-01,
            7.70442506972236706985768250888214e-01,
            7.43078833981965058974594739993336e-01,
            7.14411252525748552422157899854938e-01,
            6.84486309130959091895363144431030e-01,
            6.53360767050603974404054952174192e-01,
            6.21092608408924218288404972554417e-01,
            5.87734674344266960765992280357750e-01,
            5.53342391861581739398445733968401e-01,
            5.17979488535271648252944487467175e-01,
            4.81710877803205761438221088610590e-01,
            4.44597083516632518573885590740247e-01,
            4.06700509318326075547389564235345e-01,
            3.68090520120306408102806017268449e-01,
            3.28837429883706844346846764892689e-01,
            2.89007390856978629845031036893488e-01,
            2.48667792791365999116592888640298e-01,
            2.07891987066149058760444745530549e-01,
            1.66753930239851994032918014454481e-01,
            1.25323304735560470124511311951210e-01,
            8.36704089547703616647211788404093e-02,
            4.18707394357286030728282355539704e-02,
            0.0e+00,
            9.99676391182877210894730524159968e-01, // N = 77
            9.98049930535687690458246379421325e-01,
            9.94744779244139287754933320684358e-01,
            9.89739454266385654257476289785700e-01,
            9.83099072994788603097049417556264e-01,
            9.74846328590153965443221295572584e-01,
            9.64966573751256495583561445528176e-01,
            9.53466330933529948588045499491272e-01,
            9.40381489814268278770725828508148e-01,
            9.25741332048584664171642089058878e-01,
            9.09559042074942203370824245212134e-01,
            8.91855739004632441790931807190645e-01,
            8.72668895636572128360342048836173e-01,
            8.52035021932362468533028732053936e-01,
            8.29982434799397261748765686206752e-01,
            8.06544167605316997260445077699842e-01,
            7.81763915901667938435082305659307e-01,
            7.55685903753970822371854865195928e-01,
            7.28349806133262056562216457678005e-01,
            6.99798680379184800948166866874089e-01,
            6.70083061983433814212673951260513e-01,
            6.39254415829681565952569144428708e-01,
            6.07361590714389998346689480968053e-01,
            5.74456021047807130486262394697405e-01,
            5.40594495447936251864007317635696e-01,
            5.05834717927931554193321517232107e-01,
            4.70232884957751062771080796665046e-01,
            4.33847169432376555953112529095961e-01,
            3.96739483624291400243322414098657e-01,
            3.58972440479435161986287994295708e-01,
            3.20607811555410571191515600730781e-01,
            2.81708809790164882436158677592175e-01,
            2.42341033568550967558508091315161e-01,
            2.02570453892116503213927103388414e-01,
            1.62462620605486607328060699728667e-01,
            1.22084025337867510541123294842691e-01,
            8.15023241711042428780942259436415e-02,
            4.07851479045782880361592503959400e-02,
            0.0e+00,
            9.99692503534965415390445286902832e-01, // N = 79
            9.98147383066433024900732107198564e-01,
            9.95007423359634879389545858430211e-01,
            9.90251536854686253974477949668653e-01,
            9.83941456918198342762593711086083e-01,
            9.76098709333471314941732543957187e-01,
            9.66708343769861810912402688700240e-01,
            9.55775212324652456707951841963222e-01,
            9.43332998197736749546038481639698e-01,
            9.29409148486738279082430835842388e-01,
            9.14014488521817547450609708903357e-01,
            8.97167119292992865098312904592603e-01,
            8.78901930932081798530930427659769e-01,
            8.59252937999905874733030941570178e-01,
            8.38244768742385515380988181277644e-01,
            8.15906297430142868343239115347387e-01,
            7.92278082619136347908295192610240e-01,
            7.67401242931063154451010177581338e-01,
            7.41310715094635086508390031667659e-01,
            7.14044435894534812447886906738859e-01,
            6.85649309326793465757532430870924e-01,
            6.56173213432011070977978306473233e-01,
            6.25659418394658550788278716936475e-01,
            5.94153454957277893377920463535702e-01,
            5.61708133125002007091097766533494e-01,
            5.28377268660437326985856998362578e-01,
            4.94210838073494529432139188429574e-01,
            4.59260512309135837671902891088394e-01,
            4.23584074047897995995981546002440e-01,
            3.87240163971561468514437365229242e-01,
            3.50283891950397718861864859718480e-01,
            3.12771559248185782031725921115139e-01,
            2.74764712406530109412017282011220e-01,
            2.36325512461835696154111019495758e-01,
            1.97512603474731568420352800785622e-01,
            1.58385339997837770731337059260113e-01,
            1.19007656055122243432542461505363e-01,
            7.94438046087556498653370340434776e-02,
            3.97543267640566369558463577504881e-02,
            0.0e+00,
            9.99707559258700140247810850269161e-01, // N = 81
            9.98237709710559473208490999240894e-01,
            9.95250573446072817063168258755468e-01,
            9.90726238699457195657771535479696e-01,
            9.84722839864250243380183746921830e-01,
            9.77259949983774300896754994028015e-01,
            9.68323126854150340037108435353730e-01,
            9.57916819213792014586772438633488e-01,
            9.46071837162500095530504040652886e-01,
            9.32812808278676408590968094358686e-01,
            9.18149543072899088080873752915068e-01,
            9.02098806968874455947116075549275e-01,
            8.84692008701090104594300100870896e-01,
            8.65959503212259340543255348165985e-01,
            8.45923985587310967027008246077457e-01,
            8.24612230833311699029763985890895e-01,
            8.02060566140252562128409863362322e-01,
            7.78305651426519640168066871410701e-01,
            7.53379803438942063920080727257300e-01,
            7.27318255189927320714105007937178e-01,
            7.00162977487330140391463828564156e-01,
            6.71956684614179677872414231387665e-01,
            6.42739524305579901231055828247918e-01,
            6.12553889667980522304446822090540e-01,
            5.81447065829129638991901174449595e-01,
            5.49467125095128294809398994402727e-01,
            5.16660607386383086137016107386444e-01,
            4.83075801686178918359360068279784e-01,
            4.48764513638163831110716728289844e-01,
            4.13779204371604814038931863251491e-01,
            3.78171435473588890552321117866086e-01,
            3.41994090825758711993387350958074e-01,
            3.05302441735246787857249728403986e-01,
            2.68152185007253573978402982902480e-01,
            2.30598521880719553589500492307707e-01,
            1.92697580701371246059139252793102e-01,
            1.54506879379394418405624378465291e-01,
            1.16084070675255029980732501826424e-01,
            7.74865883312825937112577889820386e-02,
            3.87724175060509684831444587871374e-02,
            0.0e+00,
            9.99721429324918919867570821224945e-01, // N = 83
            9.98321588574771601187762826157268e-01,
            9.95476651842137405523658344463911e-01,
            9.91167109699016557478046252072090e-01,
            9.85448238798800613125195013708435e-01,
            9.78338673561083282947947736829519e-01,
            9.69823836067798761284564079687698e-01,
            9.59906891730345823710024433239596e-01,
            9.48616879571488214040186903730500e-01,
            9.35976987497853740727293825329980e-01,
            9.21995207495127644392596266698092e-01,
            9.06685944758101269869143834512215e-01,
            8.90078577248639590813183986028889e-01,
            8.72201511692441089351746086322237e-01,
            8.53074552370187033645265728409868e-01,
            8.32721200401360994725052933063125e-01,
            8.11175322139445431623983040481107e-01,
            7.88471145047409338602051320776809e-01,
            7.64637245027556033960536296945065e-01,
            7.39704803069926142278234237892320e-01,
            7.13712927612934922017018379847286e-01,
            6.86701502034951172248611328541301e-01,
            6.58706241077727683297382554883370e-01,
            6.29764839072196269675885105243651e-01,
            5.99921416448969568868676560668973e-01,
            5.69220941610215858119659060321283e-01,
            5.37704976253966959731656061194371e-01,
            5.05416599199405291997777567303274e-01,
            4.72404286698761111118471944791963e-01,
            4.38717277051406895349572323539178e-01,
            4.04401755283383568251309725383180e-01,
            3.69505022640480851325861522127525e-01,
            3.34079019574284430404986778739840e-01,
            2.98176277341824502720157852309057e-01,
            2.61846368937023177281275820860174e-01,
            2.25139605633422557051659396165633e-01,
            1.88110354745297886358557093444688e-01,
            1.50813354863992277188344814931042e-01,
            1.13300301683207080283288803457253e-01,
            7.56232589891624312761209125710593e-02,
            3.78378939143896100838482254857809e-02,
            0.0e+00,
            9.99734432248282289812379985960433e-01, // N = 85
            9.98399618990062243106820005777990e-01,
            9.95686728319411629151147735683480e-01,
            9.91577288340860785176289482478751e-01,
            9.86123534198684370544185640028445e-01,
            9.79342508063748340418896987102926e-01,
            9.71220149713752256559473607921973e-01,
            9.61759365338204719186876445746748e-01,
            9.50986859947952956062522389402147e-01,
            9.38923557354988114198590665182564e-01,
            9.25576712465747686309214259381406e-01,
            9.10959724904127354783156533812871e-01,
            8.95099182807171933617951253836509e-01,
            8.78020569812173135026966974692186e-01,
            8.59742209518730704509437146043638e-01,
            8.40285983261817026601647739880718e-01,
            8.19682375581742173054067279736046e-01,
            7.97962053255487524516809116903460e-01,
            7.75151551255706672272083324060077e-01,
            7.51279935689480260485595408681547e-01,
            7.26382365746304881071182535379194e-01,
            7.00494590556170915185418834880693e-01,
            6.73649861879432210187701457471121e-01,
            6.45883388869247565544640110601904e-01,
            6.17234850884114116809087136061862e-01,
            5.87744597485109210310838534496725e-01,
            5.57451443484292208374597521469695e-01,
            5.26395749931192313830763396254042e-01,
            4.94621159850633040910850013460731e-01,
            4.62171912070421797569252930770745e-01,
            4.29091308587839448396294983467669e-01,
            3.95423852042975199072571967917611e-01,
            3.61216369741547693728023205039790e-01,
            3.26516124465411616828447449734085e-01,
            2.91369828745837111672045693921973e-01,
            2.55825079342879013744038729782915e-01,
            2.19930967478449229668413522631454e-01,
            1.83736806564854360246386022481602e-01,
            1.47291623055288006804985911912809e-01,
            1.10645027208519916572804220322723e-01,
            7.38473616000984989238276057221810e-02,
            3.69489431653515221221084630087717e-02,
            0.0e+00,
            9.99746457530964471871470777841751e-01, // N = 87
            9.98472332242507754074267722899094e-01,
            9.95882724285588105672673009394202e-01,
            9.91959557593244056761250249110162e-01,
            9.86752630714975431658331217477098e-01,
            9.80278220980255521332935586542590e-01,
            9.72522244949065028940538013557671e-01,
            9.63486613014079784633736380783375e-01,
            9.53196590390627984668014960334403e-01,
            9.41671956847638047527482285659062e-01,
            9.28918551269247716462018615857232e-01,
            9.14947907206138832947317496291362e-01,
            8.99784996804390946323337630019523e-01,
            8.83453765218616959842279356962536e-01,
            8.65970246227808715389073768164963e-01,
            8.47353716209315099838761398132192e-01,
            8.27632708282065476801392378547462e-01,
            8.06835964136938477153648818784859e-01,
            7.84987034881737710811933084187331e-01,
            7.62111747194954891604368185653584e-01,
            7.38242982423637394973070513515268e-01,
            7.13414235268956975488663374562748e-01,
            6.87655201113672398527398854639614e-01,
            6.60997313751497839184878557716729e-01,
            6.33477715195780999302144209650578e-01,
            6.05134259639601324032298634847393e-01,
            5.76001743325693649211416413891129e-01,
            5.46116316660084533118890703917714e-01,
            5.15518923436850018404697948426474e-01,
            4.84251176785734704921537741029169e-01,
            4.52352007556055535353323193703545e-01,
            4.19861376029269317555758789239917e-01,
            3.86823366296790649432324471490574e-01,
            3.53282612864304013111649283018778e-01,
            3.19281214509383126642916295168106e-01,
            2.84861998032913399381271801757975e-01,
            2.50071400103100527356758675523452e-01,
            2.14956244860518452810538292396814e-01,
            1.79560810292162004175864353783254e-01,
            1.43929809510713241360591041484440e-01,
            1.08111163035700369450253788272676e-01,
            7.21529908745863340913118122443848e-02,
            3.61007394374324996899616735390737e-02,
            0.0e+00,
            9.99757764519839775552156879712129e-01, // N = 89
            9.98540200636773844777849262754899e-01,
            9.96065462440955173839540748303989e-01,
            9.92316392138515857013203458336648e-01,
            9.87340194175236884888136046356522e-01,
            9.81151833077913870795327966334298e-01,
            9.73737734615330086107576335052727e-01,
            9.65099650422493016144187549798517e-01,
            9.55260928192337210873574804281816e-01,
            9.44239509118193875991664754110388e-01,
            9.32040696149230352141046296310378e-01,
            9.18675259984175429650576916174032e-01,
            9.04165912394972903776135808584513e-01,
            8.88534238286043165366834273299901e-01,
            8.71795127436839734080820107919862e-01,
            8.53966595004710282701410051231505e-01,
            8.35074442856522436429145272995811e-01,
            8.15144539645135224326111256232252e-01,
            7.94198832442848723367490038071992e-01,
            7.72261479248755766668921296513872e-01,
            7.49362168787880533749046207958600e-01,
            7.25531053660716906961170025169849e-01,
            7.00795870781748986289017011586111e-01,
            6.75186070666122684080789895233465e-01,
            6.48735193430612699927451103576459e-01,
            6.21477345903576172680971012596274e-01,
            5.93445114446988553069672889250796e-01,
            5.64672453185470990533190160931554e-01,
            5.35196366644274279522619508497883e-01,
            5.05054391388202295054554724629270e-01,
            4.74283106405047449882772525597829e-01,
            4.42920174525411547428177527763182e-01,
            4.11005485816235749396696519397665e-01,
            3.78579352014707049001174254954094e-01,
            3.45681495610433653364879091896000e-01,
            3.12352466502785919288953664363362e-01,
            2.78634340176660666443808622716460e-01,
            2.44569456928201617307294668535178e-01,
            2.10199819285652844680356565731927e-01,
            1.75568014775516811898370406197500e-01,
            1.40717523161141305765298170626920e-01,
            1.05691901708653293590067789864406e-01,
            7.05345542264027153267491598853667e-02,
            3.52892369641354466947014145716821e-02,
            0.0e+00,
            9.99768258198128423330786063161213e-01, // N = 91
            9.98603645181936561137092667195247e-01,
            9.96236484002620437117059282172704e-01,
            9.92649998447203807394600971747423e-01,
            9.87889297558341872296239216666436e-01,
            9.81968715034540529096318550728029e-01,
            9.74874728599846251952953934960533e-01,
            9.66608310396894654381583222857444e-01,
            9.57191624013281616711878996284213e-01,
            9.46641690995629225824359309626743e-01,
            9.34962701708230703445678955176845e-01,
            9.22163936719000210118224458710756e-01,
            9.08266807683464127975980773044284e-01,
            8.93291671753241756093188996601384e-01,
            8.77251587193021764576883469999302e-01,
            8.60162475960664307805814132734668e-01,
            8.42048576910406909590278701216448e-01,
            8.22934220502086088977478084416362e-01,
            8.02838951166836345407773478655145e-01,
            7.81784312593906238753049819933949e-01,
            7.59798164520410823641327624500263e-01,
            7.36908848945490135839975209819386e-01,
            7.13141224275491425466100281482795e-01,
            6.88521680771200461634862222126685e-01,
            6.63081708602233588223384685989004e-01,
            6.36853394453223642379668945068261e-01,
            6.09866054493895526356084246799583e-01,
            5.82150212569353397995541854470503e-01,
            5.53740672159348856773419811361236e-01,
            5.24672820462916300598976704350207e-01,
            4.94979657498101965895642706527724e-01,
            4.64695123919634800468969615394599e-01,
            4.33856843741782960410802161277388e-01,
            4.02502943858541961663632946510916e-01,
            3.70669342359731035507763863279251e-01,
            3.38392654250602553656079862776096e-01,
            3.05712721866233050338479415586335e-01,
            2.72669769752378055027719483405235e-01,
            2.39301853204712033917900271262624e-01,
            2.05647489783263637264099088497460e-01,
            1.71748065949780898131749040658178e-01,
            1.37645205983253027248736088949954e-01,
            1.03378302832145274603448115158244e-01,
            6.89869801631440432432285092545499e-02,
            3.45134487517777116538653103816614e-02,
            0.0e+00,
            9.99778151819073701567219814023701e-01, // N = 93
            9.98663042133818290579938548034988e-01,
            9.96396428126260058633079097489826e-01,
            9.92962348906174518958778207888827e-01,
            9.88403682683398288055798275308916e-01,
            9.82733669804167098149605408252683e-01,
            9.75939278300314128067327601456782e-01,
            9.68021391853992163589737174334005e-01,
            9.59000582510578958306268759770319e-01,
            9.48892363446089848189046733750729e-01,
            9.37700536141863771888438350288197e-01,
            9.25433798806753804555569331569131e-01,
            9.12111713155850378775824083277257e-01,
            8.97752711533942315824674551549833e-01,
            8.82368961494760961628003315126989e-01,
            8.65975394866858150244581793231191e-01,
            8.48594023341959768913511652499437e-01,
            8.30246837066066167842848244617926e-01,
            8.10952109491733574841987319814507e-01,
            7.90730057075274439526424430368934e-01,
            7.69605935121729034520399181928951e-01,
            7.47605359615666653638754723942839e-01,
            7.24751619869023477882308270636713e-01,
            7.01069512020405793961685958493035e-01,
            6.76587580423016810016179078957066e-01,
            6.51334846201997552661566714959918e-01,
            6.25338836340463721796822937903926e-01,
            5.98628289712715533354980834701564e-01,
            5.71234774920969967659800659021130e-01,
            5.43190330261802412081806323840283e-01,
            5.14526028633666476785890608880436e-01,
            4.85273918388164582360388976667309e-01,
            4.55468160975091074238463306755875e-01,
            4.25143313282828061439033717761049e-01,
            3.94333316514864751223257144374656e-01,
            3.63072877020995887775711707945447e-01,
            3.31398212978702144670961615702254e-01,
            2.99345822701870045712269075011136e-01,
            2.66951828959114290107379474648042e-01,
            2.34252922206269642568798872162006e-01,
            2.01286770415851939963758354679157e-01,
            1.68091179467103307709763271304837e-01,
            1.34703753620199817575553424831014e-01,
            1.01162475305584267926128916315065e-01,
            6.75058073721548634882339001705986e-02,
            3.37721900160520283051823753339704e-02,
            0.0e+00,
            9.99787363335372880612794688204303e-01, // N = 95
            9.98718728584212067644898525031749e-01,
            9.96546543724575517586572459549643e-01,
            9.93255210987768477615134088409832e-01,
            9.88885792674205510444096489663934e-01,
            9.83451003071623697238123895658646e-01,
            9.76937911700182959329197274200851e-01,
            9.69346787326564318654220642201835e-01,
            9.60697217836146144520625966833904e-01,
            9.51003969257708692275343764777062e-01,
            9.40269961836116774378524496569298e-01,
            9.28502693012360658109116684499895e-01,
            9.15720667876155580700014979811385e-01,
            9.01941329438525118966651916707633e-01,
            8.87175367212682863815587097633397e-01,
            8.71436015796896668028637122915825e-01,
            8.54744023317656531624209037545370e-01,
            8.37120139899902193647562853584532e-01,
            8.18580687449319110982060010428540e-01,
            7.99143754167741859895102152222535e-01,
            7.78833114428370443249605159508064e-01,
            7.57672918445438714485362652339973e-01,
            7.35684106401860882229470917081926e-01,
            7.12888973409064652386746274714824e-01,
            6.89314395527633405613698869274231e-01,
            6.64987747390332728514295013155788e-01,
            6.39933874489238219140929686545860e-01,
            6.14178699956373419510669009468984e-01,
            5.87751987103851236682316994119901e-01,
            5.60684005934663942660733937373152e-01,
            5.33002879017402952932513926498359e-01,
            5.04737583863577476961381762521341e-01,
            4.75920403113300860553636084659956e-01,
            4.46584073104855372449151218461338e-01,
            4.16759379711043709271223178802757e-01,
            3.86477764084667108068771312900935e-01,
            3.55773565088884413665226702505606e-01,
            3.24681486337735913938473686357611e-01,
            2.93234353977043005201608139032032e-01,
            2.61465459214974327295522016356699e-01,
            2.29410670550207917983698280295357e-01,
            1.97106110279111595984247173873882e-01,
            1.64586006722905575649917864211602e-01,
            1.31884866554515062242458611763141e-01,
            9.90395191785916478854900901751535e-02,
            6.60869239163558025440536880523723e-02,
            3.30620601558881954673552172607742e-02,
            0.0e+00,
            9.99796069672232223801700001786230e-01, // N = 97
            9.98771007252425957467778516729595e-01,
            9.96687331944437593378438577929046e-01,
            9.93530172266350986021166136197280e-01,
            9.89338657752443673132347612408921e-01,
            9.84124583722826629106350537767867e-01,
            9.77875485474333006052916061889846e-01,
            9.70591592546247272643711312412051e-01,
            9.62291159467156820284117202390917e-01,
            9.52987703160430799087521336332429e-01,
            9.42683863363016016911899441765854e-01,
            9.31386690706554554175511384528363e-01,
            9.19113162182880749639934947481379e-01,
            9.05879136715569965865313406538917e-01,
            8.91694605580593546712009356269846e-01,
            8.76572020274247964977121228002943e-01,
            8.60530296630311331007590069930302e-01,
            8.43588261624393487281281522882637e-01,
            8.25761222530026373078726464882493e-01,
            8.07066204029442735290444943530019e-01,
            7.87524837967449320430546322313603e-01,
            7.67159032515740468838316701294389e-01,
            7.45988461809639957778017560485750e-01,
            7.24034130923814855940179313620320e-01,
            7.01320487752545629334122168074828e-01,
            6.77872379632663779602808062918484e-01,
            6.53713194553681820053725459729321e-01,
            6.28867396776513820633169871143764e-01,
            6.03362074167368755972518101771129e-01,
            5.77224726083972461410098730993923e-01,
            5.50481888618180814631841712980531e-01,
            5.23160974722233107492286308115581e-01,
            4.95291390296794198366825412449543e-01,
            4.66902904750958192003906788158929e-01,
            4.38024655410838570368525779485935e-01,
            4.08686481990716943268893146523624e-01,
            3.78919695568152803399897265990148e-01,
            3.48755886292161032535830145207001e-01,
            3.18226241206747473277971494098892e-01,
            2.87362487355455498150291759884567e-01,
            2.56197366314654950691931389883393e-01,
            2.24763790394689466634048358173459e-01,
            1.93094434019761701515349727742432e-01,
            1.61222356068891931046849208541971e-01,
            1.29181210976448440641561887787248e-01,
            9.70046992094628079961182720580837e-02,
            6.47264110276269538646332080134016e-02,
            3.23801709628692702125363211962394e-02,
            0.0e+00,
            9.99804199685638605998860839463305e-01, // N = 99
            9.98820150606635537293698234861949e-01,
            9.96819814299826467696163945220178e-01,
            9.93788661944167484030288051144453e-01,
            9.89764238414064689841609379072906e-01,
            9.84757895914213032817485782288713e-01,
            9.78757303031206671306563293910585e-01,
            9.71762200901555184273661325278226e-01,
            9.63790018136355119970914984151023e-01,
            9.54853658674136962503098402521573e-01,
            9.44955059221329274343759152543498e-01,
            9.34100294755810023339392955676885e-01,
            9.22305475453936041141389523545513e-01,
            9.09585655828073380568810080148978e-01,
            8.95949624583592951765353973314632e-01,
            8.81408445573009124984764639521018e-01,
            8.65980004315145768245542967633810e-01,
            8.49682119844165750777165158069693e-01,
            8.32528501487459937635549067636020e-01,
            8.14534427359855262018584198813187e-01,
            7.95720320762525079594240651204018e-01,
            7.76106894345446884919681451719953e-01,
            7.55711890369514471821332790568704e-01,
            7.34554254237402393101774578099139e-01,
            7.12657066705008501728002556774300e-01,
            6.90043824425132013011818798986496e-01,
            6.66735700841571632402349223411875e-01,
            6.42754832419237587259885913226753e-01,
            6.18126817800879191366902887239121e-01,
            5.92877694108900121783278791554039e-01,
            5.67031549495391362647467303759186e-01,
            5.40613246991726081880358378839446e-01,
            5.13650628401734365979791618883610e-01,
            4.86171941452491707114091923358501e-01,
            4.58203691539029622781242778728483e-01,
            4.29772993341576259318514985352522e-01,
            4.00909573929279949844328712060815e-01,
            3.71643501262285180786193450330757e-01,
            3.42003195991855746260768000865937e-01,
            3.12017532119749085861570847555413e-01,
            2.81717708241029429760970970164635e-01,
            2.51135178612577114609649697740679e-01,
            2.20299765509805400842680001005647e-01,
            1.89241592461813740166931552266760e-01,
            1.57992877664368286394491747159918e-01,
            1.26585997269672068110679674646235e-01,
            9.50516499861236013879661754799599e-02,
            6.34206849826871726927279837582319e-02,
            3.17258634590728075264287610934844e-02,
            0.0e+00,
            9.99811901364364707944787369342521e-01, // N = 101
            9.98866404420070685965526990912622e-01,
            9.96944387018876443384840513317613e-01,
            9.94031969432090822813563590898411e-01,
            9.90165010669680323296404367283685e-01,
            9.85354084048005951501636445755139e-01,
            9.79587296760769388193068607506575e-01,
            9.72864385106692153293295177718392e-01,
            9.65201651066145083213143607281381e-01,
            9.56610955242807925458237150451168e-01,
            9.47094034244939653177652871818282e-01,
            9.36656618944877616961264266137732e-01,
            9.25313546474801684738054063927848e-01,
            9.13078556655792072938027104100911e-01,
            8.99959887564294458428548750816844e-01,
            8.85967979523613058390196783875581e-01,
            8.71119198204099887128393220336875e-01,
            8.55429769429945974223983284900896e-01,
            8.38912586967224371825579964934150e-01,
            8.21582070859335766854769644851331e-01,
            8.03456868050459127594820074591553e-01,
            7.84555832900399541252056678786175e-01,
            7.64895679372351477987024281901540e-01,
            7.44494302226068382921653210360091e-01,
            7.23372766022592594836737589503173e-01,
            7.01552468706821974464560298656579e-01,
            6.79053389406747531786834315425949e-01,
            6.55896465685439244985843743052101e-01,
            6.32105068445064643967157280712854e-01,
            6.07702927184949559524795859033475e-01,
            5.82712817817836126188524303870508e-01,
            5.57158304514649982408514006237965e-01,
            5.31064824522707978893265590158990e-01,
            5.04458144907464434147925658180611e-01,
            4.77363392233042638235218646514113e-01,
            4.49806334974038601881574095386895e-01,
            4.21814157310613335738480600412004e-01,
            3.93414311897564872300137039928813e-01,
            3.64633828861614051053408047664561e-01,
            3.35500245419437514993177273936453e-01,
            3.06042119229184006456989664002322e-01,
            2.76288193779532342819749146656250e-01,
            2.46266947398144003811282232163649e-01,
            2.16007236876041841533435672317864e-01,
            1.85538581722772905058249648391211e-01,
            1.54890589998145700167953009440680e-01,
            1.24092724359160286318193300303392e-01,
            9.31747015600867395379580671033182e-02,
            6.21665648194164380258008861801500e-02,
            3.10983383271895494348591171274165e-02,
            0.0e+00,
            9.99819112765990558600037729775067e-01, // N = 103
            9.98909990848903195370667162933387e-01,
            9.97061892790189085999941198679153e-01,
            9.94261260436752225544410066504497e-01,
            9.90542561209446725811744727252517e-01,
            9.85915991735902719206308120192261e-01,
            9.80369811985698280665246784337796e-01,
            9.73903368019323756321625751297688e-01,
            9.66532262529666730266342256072676e-01,
            9.58267848613908346244727454177337e-01,
            9.49111298412882331554385473282309e-01,
            9.39067544002962550919733075716067e-01,
            9.28150705207862136703056421538349e-01,
            9.16373862309780018442495475028409e-01,
            9.03744267561153669099383023421979e-01,
            8.90271218029527466875094887654996e-01,
            8.75970232505341006579158147360431e-01,
            8.60856711182292344552990925876657e-01,
            8.44942229630138208484879669413203e-01,
            8.28239763823064967240838996076491e-01,
            8.10766967185254872063637776591349e-01,
            7.92541712099381068235004477173788e-01,
            7.73579112391981738028334802947938e-01,
            7.53895354485375368547295238386141e-01,
            7.33510375203127340526521038555074e-01,
            7.12444457577036005524462325411150e-01,
            6.90715739487578916921961535990704e-01,
            6.68343221175369928133136454562191e-01,
            6.45349038152381093702558700897498e-01,
            6.21755704600723380082172297989018e-01,
            5.97583952754948355412523142149439e-01,
            5.72855216351303542232642485032557e-01,
            5.47593624977224080474513812077930e-01,
            5.21823669366185516338418892701156e-01,
            4.95568268590575622400962174651795e-01,
            4.68850904286041147983610244409647e-01,
            4.41697422430716302166331388434628e-01,
            4.14133983226303847846594408110832e-01,
            3.86185284311379217747628445067676e-01,
            3.57876456688409227968605819114600e-01,
            3.29234735898236097195734828346758e-01,
            3.00287606335331858087300815896015e-01,
            2.71061127323951434053839193438762e-01,
            2.41581666447798659724810477200663e-01,
            2.11877487738543840434246590120893e-01,
            1.81977026957077708813059757630981e-01,
            1.51907278395672029613905351652647e-01,
            1.21695421018888833009086170022783e-01,
            9.13703630258353993731645914522232e-02,
            6.09611001505786023746402690903778e-02,
            3.04951270720150574566886803040688e-02,
            0.0e+00,
            9.99825958605753184471609529282432e-01, // N = 105
            9.98951111103950406544527140795253e-01,
            9.97172647272209999869119201321155e-01,
            9.94477590929216059834061525180005e-01,
            9.90898929927916505278062686556950e-01,
            9.86446195651550006289198790909722e-01,
            9.81108058725305931524474090110743e-01,
            9.74883884221744767550887900142698e-01,
            9.67788315389516373699052564916201e-01,
            9.59831826933086773578907013870776e-01,
            9.51015450880597801308624639204936e-01,
            9.41343853641359307182767679478275e-01,
            9.30830086101182008206933460314758e-01,
            9.19486128916425005108692403155146e-01,
            9.07318797865176551731281051615952e-01,
            8.94336890534495387861113613325870e-01,
            8.80554655409332864834937026898842e-01,
            8.65986162846067886178502703842241e-01,
            8.50642328731863406332536214904394e-01,
            8.34535432326734660790634734439664e-01,
            8.17681643545920544546845576405758e-01,
            8.00097283430468486642439529532567e-01,
            7.81796625447064630343163571524201e-01,
            7.62794995193745162254117531119846e-01,
            7.43110643846613960761260386789218e-01,
            7.22762099749983621954640966578154e-01,
            7.01766516625169423093666409840807e-01,
            6.80141904227168136998216141364537e-01,
            6.57908531247582750722813216270879e-01,
            6.35086977695245913366761669749394e-01,
            6.11696885293400938188312920829048e-01,
            5.87758604979579324378846649779007e-01,
            5.63294244766945118030321282276418e-01,
            5.38326209285827195216711515968200e-01,
            5.12876260540496620166095453896560e-01,
            4.86966745698095837546759412362007e-01,
            4.60621364092353102748234050523024e-01,
            4.33864067718762014269628934926004e-01,
            4.06718373143070577313551439146977e-01,
            3.79208269116093732442607233679155e-01,
            3.51358750909551098562388915524934e-01,
            3.23195003434807837106035321994568e-01,
            2.94741926173722801340915111723007e-01,
            2.66024783605001813313606362498831e-01,
            2.37069537757488429940977425758319e-01,
            2.07902264156365673697379747864034e-01,
            1.78548866175569198588846120401286e-01,
            1.49035508606948974286154907531454e-01,
            1.19388766921929054265483216568100e-01,
            8.96352446489004223151297878757759e-02,
            5.98014644188371788380287341624353e-02,
            2.99141097973383701669192191729962e-02,
            0.0e+00,
            9.99832384738033597137984997971216e-01, // N = 107
            9.98989947776328324202665953635005e-01,
            9.97277351123438626778749949153280e-01,
            9.94681919308007533864213201013627e-01,
            9.91235411120107601234963112801779e-01,
            9.86947035023371777029410623072181e-01,
            9.81805625337224818771630907576764e-01,
            9.75810233714985097996930107910885e-01,
            9.68974906490348009135971096839057e-01,
            9.61309694623136312685574011993594e-01,
            9.52815174340658432861062010488240e-01,
            9.43495353464442354507468735391740e-01,
            9.33362684473861281553297430946259e-01,
            9.22428603042812378376424931047950e-01,
            9.10699111184307463773279778251890e-01,
            8.98182057875426931303763922187500e-01,
            8.84890990273399680177135451231152e-01,
            8.70839297558241520746946662256960e-01,
            8.56036800652357321439467341406271e-01,
            8.40494576545801619360531731217634e-01,
            8.24227972761158889092314439039910e-01,
            8.07252498416895725164010855223751e-01,
            7.89581092738756873394834201462800e-01,
            7.71227654925532357665929339418653e-01,
            7.52209500084542903586282136529917e-01,
            7.32544230807510521330527808459010e-01,
            7.12247460236342666561881742381956e-01,
            6.91335575601366714160178617021302e-01,
            6.69827815209352417369359500298742e-01,
            6.47743743916510239522210667928448e-01,
            6.25101287234140157167416873562615e-01,
            6.01919005713769661447543057875009e-01,
            5.78217909362410575901947140664561e-01,
            5.54019328277068012766903848387301e-01,
            5.29343163098038194114280940993922e-01,
            5.04209831657133733529008168261498e-01,
            4.78641899588388042285913570594857e-01,
            4.52662219461845760637430657880032e-01,
            4.26292331993750106544638356353971e-01,
            3.99554186953953061056665774231078e-01,
            3.72471646187148619500106860868982e-01,
            3.45068808495722412210682250588434e-01,
            3.17368513608647651036420711534447e-01,
            2.89393906451626048426106763145071e-01,
            2.61169855111708648642832031327998e-01,
            2.32721403724272662971728209413413e-01,
            2.04072341864729916993681513304182e-01,
            1.75246662155325721998977428484068e-01,
            1.46269927516438108527907502320886e-01,
            1.17167809071955383859453547756857e-01,
            8.79646898408178723460792980404221e-02,
            5.86850543002596578001650584610616e-02,
            2.93548347565188230690047532789322e-02,
            0.0e+00,
            9.99838496991500957911114255693974e-01, // N = 109
            9.99026666867340762401283882354619e-01,
            9.97376257556823131444900809583487e-01,
            9.94875117018338972485480553586967e-01,
            9.91553698211184442179444431531010e-01,
            9.87420637397343425867290989117464e-01,
            9.82465151950908555100738794862991e-01,
            9.76686328857903185429734094213927e-01,
            9.70097391469713077327696737484075e-01,
            9.62707645785923493697566755145090e-01,
            9.54517572854841733764885702839820e-01,
            9.45530975164995735049444647302153e-01,
            9.35759401075758279198169020673959e-01,
            9.25213359866651430252204590942711e-01,
            9.13898506039289570956896113784751e-01,
            9.01822286284701291059207051148405e-01,
            8.88997178496309548023646129877307e-01,
            8.75435454065568774417727127001854e-01,
            8.61146397234632821060529295209562e-01,
            8.46140515970772555398582426278153e-01,
            8.30431910430066477779575961903902e-01,
            8.14034785913567704440652050834615e-01,
            7.96961390914122658202245474967640e-01,
            7.79224915346254154435712280246662e-01,
            7.60841255928319748491617247054819e-01,
            7.41826538809184032885468695894815e-01,
            7.22195561816759812323596179339802e-01,
            7.01963889719172673409275375888683e-01,
            6.81149186997542011035022824216867e-01,
            6.59769387631983339481678285665112e-01,
            6.37841506713889505597592233243631e-01,
            6.15383198331127312386001904087607e-01,
            5.92413763456913988747487564978655e-01,
            5.68952768195209790391686510702129e-01,
            5.45019138816307258110782640869729e-01,
            5.20632334385933037701477132941363e-01,
            4.95813099347452879150921489781467e-01,
            4.70582412481382328373058498982573e-01,
            4.44960809469015783346179659929476e-01,
            4.18969263255204171780832211879897e-01,
            3.92629727027398955918613410176476e-01,
            3.65964340372190832795240567065775e-01,
            3.38994942740873717035299250710523e-01,
            3.11743720834467996638750264537521e-01,
            2.84233571955057440217018438488594e-01,
            2.56487520069996810523349495269940e-01,
            2.28528396646337894626554998467327e-01,
            2.00379293606213509937319372511411e-01,
            1.72063765976273014279840367635188e-01,
            1.43605427316255751524209927083575e-01,
            1.15027783942082142965013247248862e-01,
            8.63545182632479008111303642181156e-02,
            5.76095412484042002088102663037716e-02,
            2.88167481993414215102333741924667e-02,
            0.0e+00,
            9.99844247854056455970805927790934e-01, // N = 111
            9.99061419564818642413683846825734e-01,
            9.97469953387629004737391369417310e-01,
            9.95057977847412122862635897035943e-01,
            9.91854854685616071918730085599236e-01,
            9.87868941198889349841749663028168e-01,
            9.83089623421721348073276658396935e-01,
            9.77515735503988958399190778436605e-01,
            9.71159987429690008120530819724081e-01,
            9.64031328593135117266399447544245e-01,
            9.56129870134652115609696920728311e-01,
            9.47458868041210822141806602303404e-01,
            9.38029367680076719970827525685309e-01,
            9.27851424720791739808589682070306e-01,
            9.16930017610292913410319215472555e-01,
            9.05271800743999932592487311922014e-01,
            8.92888667147356818176717752066907e-01,
            8.79792322419895689300517460651463e-01,
            8.65991135401215306188760223449208e-01,
            8.51494606617154925487511718529277e-01,
            8.36316151070498836617161941831000e-01,
            8.20469298559321047470405119383940e-01,
            8.03965178084336096198114773869747e-01,
            7.86815781127622404511612330679782e-01,
            7.69036222838821337255410526267951e-01,
            7.50641856348021607736598070914624e-01,
            7.31646182790427701547741889953613e-01,
            7.12063399986637701744029982364736e-01,
            6.91910308531763162953609480609884e-01,
            6.71203990319826027111105304356897e-01,
            6.49960011187695307910416886443272e-01,
            6.28194512249927727864928783674259e-01,
            6.05925868530523548116661913809367e-01,
            5.83172738026031867164533650793601e-01,
            5.59952469474765179846542650921037e-01,
            5.36282885908343276426535339851398e-01,
            5.12183768360713331802003267512191e-01,
            4.87675158187473589688210040549166e-01,
            4.62775909679958630249529960565269e-01,
            4.37505260037174437126594739311258e-01,
            4.11884189528080923992092721164227e-01,
            3.85933900740979385357576347814756e-01,
            3.59674472333918637811933649572893e-01,
            3.33126278890023941325893019893556e-01,
            3.06311265931144161012156246215454e-01,
            2.79251553200806246213261374577996e-01,
            2.51968156052061742489200923955650e-01,
            2.24482300647845550711778628283355e-01,
            1.96816644257305217724507429011283e-01,
            1.68993963646873357475897137192078e-01,
            1.41035916797047605752979393400892e-01,
            1.12964288059329065472269348902046e-01,
            8.48021794792412353380939293856500e-02,
            5.65727538183364089818816466959106e-02,
            2.82980127344324081106741175517527e-02,
            0.0e+00,
            9.99849727701272672497623261733679e-01, // N = 113
            9.99094343801465445409348831162788e-01,
            9.97558643017585011669723371596774e-01,
            9.95231226081069730859951505408389e-01,
            9.92140296283393618992363371944521e-01,
            9.88293715540161543664510190865258e-01,
            9.83681226358892768502073522540741e-01,
            9.78301709140256603447483030322473e-01,
            9.72167163223401575855575629248051e-01,
            9.65285901905490129060183335241163e-01,
            9.57657974899251973610603272391018e-01,
            9.49286479561962992512746950524161e-01,
            9.40181691354067039512187875516247e-01,
            9.30352880247496294430220586946234e-01,
            9.19804746997011868359095387859270e-01,
            9.08543620420655617664351666462608e-01,
            8.96580487561356997971984128525946e-01,
            8.83926108327827808608390114386566e-01,
            8.70588412638168884782885470485780e-01,
            8.56576433762749056555207971541677e-01,
            8.41902531226671468900235595356207e-01,
            8.26579132142881811695644955761964e-01,
            8.10616794710246946209508678293787e-01,
            7.94026922893866782260374748148024e-01,
            7.76823431109068818223306607251288e-01,
            7.59020422705128594564882860140642e-01,
            7.40630719964353811946011774125509e-01,
            7.21667834450188117045854596653953e-01,
            7.02147232370385232513854134595022e-01,
            6.82084612694471070781787602754775e-01,
            6.61494777796274080472471723624039e-01,
            6.40393106807006895486722442001337e-01,
            6.18796522289203010380731484474381e-01,
            5.96722182770663245321429712930694e-01,
            5.74186613536352252751271407760214e-01,
            5.51206824855534627261022251332179e-01,
            5.27801045241467758906139806640567e-01,
            5.03987718384381611080868879071204e-01,
            4.79784841393908645379440258693649e-01,
            4.55210814878459546495292897816398e-01,
            4.30284986026011395665591408032924e-01,
            4.05026880927091159634301220648922e-01,
            3.79455715295564433020558681164403e-01,
            3.53591032174954633671148940265994e-01,
            3.27453083667926803101977384358179e-01,
            3.01062253867220630532131053769263e-01,
            2.74438719000083708454695852196892e-01,
            2.47602909434337076222121254431840e-01,
            2.20575748906897434187257545090688e-01,
            1.93378238635275478962682882411173e-01,
            1.66031252361970665942791924862831e-01,
            1.38555846810376304123479940244579e-01,
            1.10973369857817541483946399694105e-01,
            8.33051868224354424841138211377256e-02,
            5.55726024759832515353963344750809e-02,
            2.77970352872756037987400645761227e-02,
            0.0e+00,
            9.99854894687858819501968810072867e-01, // N = 115
            9.99125565625262779256843259645393e-01,
            9.97642821235557586412312502943678e-01,
            9.95395523678430427239050004573073e-01,
            9.92410902746466483392850932432339e-01,
            9.88696577650222119260092767945025e-01,
            9.84242460410267527848304780491162e-01,
            9.79047226709469309291478111845208e-01,
            9.73122431304167201382426810596371e-01,
            9.66476085171886878377733864908805e-01,
            9.59107936500770974497243059886387e-01,
            9.51020626447876771258904682326829e-01,
            9.42224004691850636206140734429937e-01,
            9.32726961067101845159754702763166e-01,
            9.22533631336081350049482807662571e-01,
            9.11649678521391004792917556187604e-01,
            9.00085598710066991934297675470589e-01,
            8.87851678882221384547790421493119e-01,
            8.74955079071092045595037234306801e-01,
            8.61403983262046923918830998445628e-01,
            8.47210176685496585413659431651467e-01,
            8.32385521150439511295360262010945e-01,
            8.16939630046407683217069006786915e-01,
            8.00882894547218393554999238403980e-01,
            7.84228572848437277542643641936593e-01,
            7.66990119359450495117869195382809e-01,
            7.49179258825715121972166343766730e-01,
            7.30808344744523608049746599135688e-01,
            7.11892115406623671169938916136744e-01,
            6.92445551199517894680468543811003e-01,
            6.72482224206294443291653806227259e-01,
            6.52016228280976939402080461150035e-01,
            6.31063701810954391646646399749443e-01,
            6.09641032908715407856448109669145e-01,
            5.87763403337325129882628971245140e-01,
            5.65446429269236716663726838305593e-01,
            5.42707517864783994809840805828571e-01,
            5.19564311391187527711110760719748e-01,
            4.96033369800928214399249327470898e-01,
            4.72131609517975669998435250818147e-01,
            4.47877541072230322960479043103987e-01,
            4.23289881451563765324408450396731e-01,
            3.98386335255423662538021289947210e-01,
            3.73184890086593945568438357440755e-01,
            3.47704970207239949520072741506738e-01,
            3.21966168395378227184977504293784e-01,
            2.95987095315011106144709174259333e-01,
            2.69786573161838683088120660613640e-01,
            2.43384732641507312012052466343448e-01,
            2.16801828796123863263289877068019e-01,
            1.90057134279709577517891716524900e-01,
            1.63170062591264264373336345670396e-01,
            1.36161230978666281110633917705854e-01,
            1.09051332808787634909286623496882e-01,
            8.18600540328312115123665648752649e-02,
            5.46071510016465644365979414942558e-02,
            2.73134992669634146800206053740112e-02,
            0.0e+00,
            9.99859826449020050453952990210382e-01, // N = 117
            9.99155200407386479000138024275657e-01,
            9.97722653989439822730389550997643e-01,
            9.95551476597290818659757860586978e-01,
            9.92667865432662055447110560635338e-01,
            9.89079008248442415052181786450092e-01,
            9.84775148347481366073452591081150e-01,
            9.79755014694350223614094375079731e-01,
            9.74029544612234343681222981103929e-01,
            9.67606202502923951058733109675813e-01,
            9.60484700511014533041986851458205e-01,
            9.52667557518869112520576436509145e-01,
            9.44163963446301823800865804514615e-01,
            9.34982137588259321070438545575598e-01,
            9.25125993163076643099884677212685e-01,
            9.14600928564352377847512798325624e-01,
            9.03416667513910032205615152633982e-01,
            8.91582692022030554035438854043605e-01,
            8.79105801417309762335605682892492e-01,
            8.65993794074807476945920825528447e-01,
            8.52257556804856264420777733903378e-01,
            8.37908013339372925720738294330658e-01,
            8.22954303007449095019865126232617e-01,
            8.07406327913088306402755733870436e-01,
            7.91276323986599416926424055418465e-01,
            7.74576681749652551367546493565897e-01,
            7.57318558012922804500988149811747e-01,
            7.39513731020042031083505662536481e-01,
            7.21175801585986597785904450574890e-01,
            7.02318571153908055570980195625452e-01,
            6.82954968823778152398062957217917e-01,
            6.63098445332125141504775456269272e-01,
            6.42763898439352110436573184415465e-01,
            6.21966435263078820661064582964173e-01,
            6.00720539162537092714444497687509e-01,
            5.79041135130225259608494070562301e-01,
            5.56944300711045836571599920716835e-01,
            5.34446309648847872608712350483984e-01,
            5.11562988962252607194614029140212e-01,
            4.88310537216718187902841918912600e-01,
            4.64706061824322724795877093129093e-01,
            4.40766839186839565201125878957100e-01,
            4.16509828690222960734246271385928e-01,
            3.91952296330753180431116788895451e-01,
            3.67112205963718629675440752180293e-01,
            3.42007653597995564531686341069872e-01,
            3.16656515968480156697495431217249e-01,
            2.91076914311109324895454619763768e-01,
            2.65287478030947765361702295194846e-01,
            2.39306924966153522493783611935214e-01,
            2.13153829911464171020796243283257e-01,
            1.86846951835761582172423800329852e-01,
            1.60405381814621633695949753928289e-01,
            1.33848250595466650159082178106473e-01,
            1.07194608263487964339155666948500e-01,
            8.04636302141423925826657637117023e-02,
            5.36746560008261944241247931586258e-02,
            2.68470123659424186879363105617813e-02,
            0.0e+00,
            9.99864485999864660570324303989764e-01, // N = 119
            9.99183353909294691419518130715005e-01,
            9.97798561090643354454243763029808e-01,
            9.95699640383245987429461365536554e-01,
            9.92911916659194870860005721624475e-01,
            9.89442365133731072113221216568490e-01,
            9.85281396661880193299509755888721e-01,
            9.80427573956715758818347694614204e-01,
            9.74891446852234833109207556844922e-01,
            9.68680221681781583598080942465458e-01,
            9.61793363870761974787626513716532e-01,
            9.54233009376951435420721736591076e-01,
            9.46007985309327059653128344507422e-01,
            9.37126190353453569770181275089271e-01,
            9.27591062944103317278177200932987e-01,
            9.17407438788155227271658986865077e-01,
            9.06584626937524951095781489129877e-01,
            8.95131711743472280318201228510588e-01,
            8.83054841403417944967202402040130e-01,
            8.70361094292882442324810199352214e-01,
            8.57060873086851637836502959544305e-01,
            8.43164625816872237429322467505699e-01,
            8.28680690050779378275080944149522e-01,
            8.13618107288211267480448896094458e-01,
            7.97988559567177402342963432602119e-01,
            7.81803889862361156559700248180889e-01,
            7.65074321108725863282984391844366e-01,
            7.47810645278640606647968525066972e-01,
            7.30025846901660835364111790113384e-01,
            7.11733118677198017820728637161665e-01,
            6.92944340065247521565083843597677e-01,
            6.73671864504937212281276970315957e-01,
            6.53929922889664339002990800508996e-01,
            6.33732966238849892981477296416415e-01,
            6.13094328338653959953319372289116e-01,
            5.92027740704030080998165885830531e-01,
            5.70548578313916920912163277535001e-01,
            5.48672427808396534487656026612967e-01,
            5.26413882543813826941914157941937e-01,
            5.03787866557718233551099729083944e-01,
            4.80810766222562524507821990482626e-01,
            4.57499158253266813289883430115879e-01,
            4.33868700218387415290521857968997e-01,
            4.09935317810419252992915062350221e-01,
            3.85716254483585652135246846228256e-01,
            3.61228914169794967925497530814027e-01,
            3.36489819509034782107903538417304e-01,
            3.11515700803013495523430265166098e-01,
            2.86324488375485852742485803901218e-01,
            2.60934237342811625737226677301805e-01,
            2.35362131666981638788982422738627e-01,
            2.09625503392036560690314672683598e-01,
            1.83742787853736933012527288155979e-01,
            1.57732505587858146123281244399550e-01,
            1.31612293928506179918613838708552e-01,
            1.05399879016344150128858814241539e-01,
            7.91140112194403666290298815511051e-02,
            5.27734840883100908559555364263360e-02,
            2.63961772670387659345259123711003e-02,
            0.0e+00,
            9.99868940397354744042957008787198e-01, // N = 121
            9.99210123227435853543454413738800e-01,
            9.97870677972810815603565970377531e-01,
            9.95840525118838137963450662937248e-01,
            9.93144065090209360313622255489463e-01,
            9.89787895222221880686674921889789e-01,
            9.85762734034170584607181808678433e-01,
            9.81067201752598094799395767040551e-01,
            9.75711308690630829687506775371730e-01,
            9.69701788765052641316799508786062e-01,
            9.63038090441001637387330447381828e-01,
            9.55722255839995926685048743820516e-01,
            9.47762543370821441968132603506092e-01,
            9.39166276116423337505523250001715e-01,
            9.29936713783543367206618768250337e-01,
            9.20078476177627391230373632424744e-01,
            9.09600210102026740521807823824929e-01,
            8.98510310810045731422235348873073e-01,
            8.86814628766955048710940445744200e-01,
            8.74519922646898484330790779495146e-01,
            8.61635826127129189622166904882761e-01,
            8.48171984785929811145877010858385e-01,
            8.34136340635023287859439733438194e-01,
            8.19537526162145479879939102829667e-01,
            8.04386348421674890474264429940376e-01,
            7.88693739932263659930811172671383e-01,
            7.72469446343257204468102372629801e-01,
            7.55723775306585521249758130579721e-01,
            7.38468736789273050291626532271039e-01,
            7.20716513355730614698302360920934e-01,
            7.02478440712774987453315134189324e-01,
            6.83766327381355343284496939304518e-01,
            6.64593339488917966839665041334229e-01,
            6.44972828489476568414318080613157e-01,
            6.24917533728280072402583300572587e-01,
            6.04440597048510275257626744860318e-01,
            5.83556249655679537546859592112014e-01,
            5.62278900753944377299831103300676e-01,
            5.40622515318440521880916094232816e-01,
            5.18601400058569916851070047414396e-01,
            4.96230730931717545217907172627747e-01,
            4.73525841761707255717084308344056e-01,
            4.50501745628638761154149960930226e-01,
            4.27173741583078470096523915344733e-01,
            4.03557809082794538557692476388183e-01,
            3.79670056576798142788931045288336e-01,
            3.55526365012931999665113380615367e-01,
            3.31142848268448197757152229314670e-01,
            3.06536132423845697481112893001409e-01,
            2.81722937423261932110563066089526e-01,
            2.56719828242537528861788587164483e-01,
            2.31543551376029554944580013398081e-01,
            2.06211210860876931194596295426891e-01,
            1.80739964873425501545867177810578e-01,
            1.55146875314619403507521155916038e-01,
            1.29449135396945080866970556598972e-01,
            1.03664149738055655358692774825613e-01,
            7.78093339495365687863426273906953e-02,
            5.19020575387993676752529381701606e-02,
            2.59597723012477965554012371285353e-02,
            0.0e+00,
            9.99873156841666665961554372188402e-01, // N = 123
            9.99235597631363381410096735635307e-01,
            9.97939362912048655296359811472939e-01,
            9.95974599815120154033820654149167e-01,
            9.93364923890532991457291700498899e-01,
            9.90116745232517247998771381389815e-01,
            9.86220946061099223989288020675303e-01,
            9.81676011284037142168301670608344e-01,
            9.76491611476062559837885146407643e-01,
            9.70674258833183034589353610499529e-01,
            9.64223199293384292118958001083229e-01,
            9.57140151912984293858244200237095e-01,
            9.49433064026402484536504289280856e-01,
            9.41108986681361003867607450956712e-01,
            9.32170778558261137192175738164224e-01,
            9.22622581382954942696983380301390e-01,
            9.12472689684431403911446523125051e-01,
            9.01729162474001366689435599255376e-01,
            8.90397296633347767880195533507504e-01,
            8.78483237214880974264019641850609e-01,
            8.65996207556978703223649063147604e-01,
            8.52945450847663377835772280377569e-01,
            8.39338225221052502966756492241984e-01,
            8.25182428108660159793430466379505e-01,
            8.10488396698326396538902827160200e-01,
            7.95266599282359432088185258180602e-01,
            7.79525982934400674118080587504664e-01,
            7.63276011172312029984254877490457e-01,
            7.46528169802813335031999031343730e-01,
            7.29294123449465536701552537124371e-01,
            7.11584308053892944379015261802124e-01,
            6.93409590894490612811296159634367e-01,
            6.74782568703803486975800751679344e-01,
            6.55716032095070788798807370767463e-01,
            6.36221732403661754950974227540428e-01,
            6.16311785197921735424131384206703e-01,
            5.95999818721726248860193209111458e-01,
            5.75299651350830498763855302968295e-01,
            5.54224184709951606109257227217313e-01,
            5.32786626502925186876780117017915e-01,
            5.11001529803897236448051444313023e-01,
            4.88883622262252126589032741321716e-01,
            4.66446791250155978758584751631133e-01,
            4.43705176538531753660521417259588e-01,
            4.20674130015539771143551206478151e-01,
            3.97369154725756679180648234250839e-01,
            3.73804956537792554271959488687571e-01,
            3.49996442204067115255838871235028e-01,
            3.25959622107470647911497962923022e-01,
            3.01710628963030746962914463438210e-01,
            2.77264816096504940201583622183534e-01,
            2.52637687169053049007771960532409e-01,
            2.27845760080053222340623619857070e-01,
            2.02905642518058815237935732511687e-01,
            1.77833160508530901955381864354422e-01,
            1.52644240230815381176299183607625e-01,
            1.27355748407546320866146061234758e-01,
            1.01984606562274149332836259418400e-01,
            7.65469356526298355669624129404838e-02,
            5.10589067079742220389704243643791e-02,
            2.55375714453470840925586315961482e-02,
            0.0e+00
        };

        public static readonly double[] KronrodWeight =
        {
            5.55555555555555802271783250034787e-01, // N = 3
            8.88888888888888839545643349993043e-01,
            1.97979797979798310958443607887602e-01, // N = 5
            4.90909090909090739529574420885183e-01,
            6.22222222222222343113173792517046e-01,
            1.04656226026467708001277401308471e-01, // N = 7
            2.68488089868333834608904453489231e-01,
            4.01397414775962579902568450052058e-01,
            4.50916538658474641554363415707485e-01,
            6.29773736654729299200283776372089e-02, // N = 9
            1.70053605335722224367600574623793e-01,
            2.66798340452284177271025100708357e-01,
            3.26949189601452139264381457905984e-01,
            3.46442981890136114664358046866255e-01,
            4.25820367510814992706436044045404e-02, // N = 11
            1.15233316622473352941469215693360e-01,
            1.86800796556492704203478183444531e-01,
            2.41040339228647398917004807117337e-01,
            2.72849801912559364325261412886903e-01,
            2.82987417857491263539770898205461e-01,
            3.03961541198198813285014097118619e-02, // N = 13
            8.36944404469071312480110691467416e-02,
            1.37320604634446341574260941342800e-01,
            1.81071994323137114291100147056568e-01,
            2.13209652271962923908432685493608e-01,
            2.33770864116994686598971497915045e-01,
            2.41072580173465278452482607463025e-01,
            2.29353220105290855901358781920862e-02, // N = 15
            6.30920926299782247603786800027592e-02,
            1.04790010322249771412828067695955e-01,
            1.40653259715525863482454838049307e-01,
            1.69004726639266911192294173815753e-01,
            1.90350578064785225240740373919834e-01,
            2.04432940075298913429335811997589e-01,
            2.09482141084727430113687773882702e-01,
            1.78223833207103513065483468835737e-02, // N = 17
            4.94393950021396119676175828772102e-02,
            8.24822989313585691606434124878433e-02,
            1.11646370826840243828392829072982e-01,
            1.36263109255171682709928404619859e-01,
            1.56652606168187102930744458717527e-01,
            1.72070608555212584134253006595827e-01,
            1.81400025068034459474475283968786e-01,
            1.84446405744691427353032509017794e-01,
            1.43047756438394544492576088146052e-02, // N = 19
            3.96318951602609714779390515104751e-02,
            6.65181559402738958874934382947686e-02,
            9.07906816887268930393872778950026e-02,
            1.11789134684419061427362862559676e-01,
            1.30001406855340173596147224088782e-01,
            1.45239588384365431172895455347316e-01,
            1.56413527788484357783360678695317e-01,
            1.62862827440115903732120727909205e-01,
            1.64896012828349813883477281706291e-01,
            1.16946388673721448497877517525012e-02, // N = 21
            3.25581623079650439578358600556385e-02,
            5.47558965743512385260238772843877e-02,
            7.50396748109193878484290962660452e-02,
            9.31254545836976144190799686839455e-02,
            1.09387158802297462800723337750242e-01,
            1.23491976262065136782375418533775e-01,
            1.34709217311474449552122223394690e-01,
            1.42775938577059724465811996196862e-01,
            1.47739104901337736652777721246821e-01,
            1.49445554002917535552086292227614e-01,
            9.76544104596046430577516161974927e-03, // N = 23
            2.71565546821052362924664436150124e-02,
            4.58293785644262596790099451027345e-02,
            6.30974247503747198706491872144397e-02,
            7.86645719322274644680348387737467e-02,
            9.29530985969004713842522846789507e-02,
            1.05872074481388703248718741178891e-01,
            1.16739502461048444414970504112716e-01,
            1.25158799100319434449701816447487e-01,
            1.31280684229804434082211628265213e-01,
            1.35193572799884670354586546636710e-01,
            1.36577794711118527537507816305151e-01,
            8.25771143316878473983333464047973e-03, // N = 25
            2.30360840389826869445411006154245e-02,
            3.89152304692995665291732620971743e-02,
            5.36970176077564489980353812370595e-02,
            6.72509070508397616139362185094797e-02,
            7.99202753336016175067513245267037e-02,
            9.15494682950501043050550720181491e-02,
            1.01649732279059809569865535650024e-01,
            1.10022604977644142265624793708412e-01,
            1.16712053501756771178854421577853e-01,
            1.21626303523947362772439362288424e-01,
            1.24584164536156449809567448028247e-01,
            1.25556893905473809791573103211704e-01,
            7.08784635124846355141992049198052e-03, // N = 27
            1.97537463827065877530753112978346e-02,
            3.34435899895524704761307077660604e-02,
            4.62790179738298765310666738059808e-02,
            5.81152104231143842860696224761341e-02,
            6.93036332477813266095267863420304e-02,
            7.98059621694767046262697363090410e-02,
            8.91684418775404441515064490886289e-02,
            9.71417348760790222428340712212957e-02,
            1.03830601169039679620986760255619e-01,
            1.09266351095285305095039518619160e-01,
            1.13210259171529881161433195302379e-01,
            1.15488799091286301057301955097500e-01,
            1.16209612363060474371501129553508e-01,
            6.13955868637816679772578609686207e-03, // N = 29
            1.71484589099355280716885374658887e-02,
            2.90487012615084326527803426643004e-02,
            4.02505948726886303434824299074535e-02,
            5.06915432604655991077891030727187e-02,
            6.06671258667422844124139658106287e-02,
            7.01029790027480753655808598523436e-02,
            7.86557972496214341528997238128795e-02,
            8.61837628694576418642014914439642e-02,
            9.27368300178544185952134171202488e-02,
            9.82649264721037057901398270587379e-02,
            1.02616627321400769035086852909444e-01,
            1.05731639841764077369923313653999e-01,
            1.07626421114118631106038037614780e-01,
            1.08270066506429230024366461293539e-01,
            5.37747987292346019128075340631767e-03, // N = 31
            1.50079473293151695323377481372518e-02,
            2.54608473267151740049296648749078e-02,
            3.53463607913763536161333433938125e-02,
            4.45897513247650728596127578384767e-02,
            5.34815246909283378839994327336171e-02,
            6.20095678006703857065851082097652e-02,
            6.98541213187276466278774478269042e-02,
            7.68496807577201124228594153464655e-02,
            8.30805028231330067178816989326151e-02,
            8.85644430562117918048770093264466e-02,
            9.31265981708242762682203874646802e-02,
            9.66427269836229174693187360389857e-02,
            9.91735987217921693970268393059087e-02,
            1.00769845523875550830084080189408e-01,
            1.01330007014790793307135174927680e-01,
            4.74277704924697899452334937109299e-03, // N = 33
            1.32579306880912708294095736505369e-02,
            2.24988594400489447244773089096270e-02,
            3.12605436473811573727665802380216e-02,
            3.95129512024209178511213735873753e-02,
            4.75062159764066058165177253158618e-02,
            5.52056330954225488172326663516287e-02,
            6.23588060118346679261414067241276e-02,
            6.88629951915312038535077476808510e-02,
            7.47698238855998703611405176161497e-02,
            8.00539412637194525146355772449169e-02,
            8.45958037925919476007763364577841e-02,
            8.83375025791130336072498607791204e-02,
            9.12920328281904974732086088806682e-02,
            9.34386740609211147168267075358017e-02,
            9.47284012472300179785733575954509e-02,
            9.51542160804982745103686170295987e-02,
            4.21897579377691900326396989839850e-03, // N = 35
            1.17858375622883811834062939283285e-02,
            2.00222339532946207174557429198103e-02,
            2.78567224578629146769515045889420e-02,
            3.52497467518806256725483194713888e-02,
            4.24426302050016288069933523274813e-02,
            4.94361418239588831791131440240861e-02,
            5.59940445300942321593673511870293e-02,
            6.20009152682301292736077868994471e-02,
            6.75280167181304402657104901663843e-02,
            7.25898901141902724853949280259258e-02,
            7.70562230462022296206825444642163e-02,
            8.08366784408182520449415164875973e-02,
            8.39725719912355339502596507372800e-02,
            8.64905322056510050821032109524822e-02,
            8.83087822976041658673551637548371e-02,
            8.93618458677885862950773798729642e-02,
            8.96964219439821547341651353235648e-02,
            3.77351012844074100091584789140597e-03, // N = 37
            1.05544305675438383762543281818580e-02,
            1.79333762057115979338117739416703e-02,
            2.49644027537403480343503048288767e-02,
            3.16340198488447715829963158284954e-02,
            3.81537583251759099267630404028750e-02,
            4.45091951650895267800223109588842e-02,
            5.05075715021018889494541781459702e-02,
            5.60723903829939418486105751071591e-02,
            6.12535657913583428402226616071857e-02,
            6.60399581928171192091170382809651e-02,
            7.03374500242248956727308950576116e-02,
            7.40970273813158775144671608359204e-02,
            7.73320701646387637095969580514065e-02,
            8.00300194950957916040223949494248e-02,
            8.21439997833294244244939363852609e-02,
            8.36548514371627388586105666945514e-02,
            8.45693335440753507503686137170007e-02,
            8.48781386126768178090884475750499e-02,
            3.39815311963492837701861226662459e-03, // N = 39
            9.49920546171027432857947303546098e-03,
            1.61534143690916995317330417947232e-02,
            2.25086957522035689682748937912038e-02,
            2.85442381171149145435705918316671e-02,
            3.44623528628813236007744080779958e-02,
            4.02700232495143625732758607682626e-02,
            4.57859730879225448885172511381825e-02,
            5.09262255062440383213129280193243e-02,
            5.57522010334808443277054834652517e-02,
            6.02774115032086166277025540694012e-02,
            6.44023522619290161861371757368033e-02,
            6.80597804981340898100583558516519e-02,
            7.12814247649301430120871714279929e-02,
            7.40840745337379008583766903939249e-02,
            7.64028619398165881326789872218797e-02,
            7.81869106857413648237198344759236e-02,
            7.94656835853552179216308104514610e-02,
            8.02662160208506003655770655313972e-02,
            8.05456032929982579382510721188737e-02,
            3.07358371851970246096952266157132e-03, // N = 41
            8.60026985564303798892371588635797e-03,
            1.46261692569714871203778727704048e-02,
            2.03883734612666754626442155995392e-02,
            2.58821336049522253419663542217677e-02,
            3.12873067770326196423980036342982e-02,
            3.66001697582009968834348967448022e-02,
            4.16688733279727760439037353989988e-02,
            4.64348218674976512265750727692648e-02,
            5.09445739237290168288652125738736e-02,
            5.51951053482847564524149674980436e-02,
            5.91114008806389937267233847251191e-02,
            6.26532375547814990301986881604535e-02,
            6.58345971336182639310763420326111e-02,
            6.86486729285213093110229465310113e-02,
            7.10544235534444207358362177728850e-02,
            7.30306903327871265174664472397126e-02,
            7.45828754004993627058084371128643e-02,
            7.57044976845567124668079372895590e-02,
            7.63778676720801019683904087287374e-02,
            7.66007119180001361247178692792659e-02,
            2.79548123241232099323028137405345e-03, // N = 43
            7.81833730212382581326036046220906e-03,
            1.33046426070887128384478970133387e-02,
            1.85600554088754185477760927369673e-02,
            2.35741990830289349645454421988688e-02,
            2.85184265702047093360427254538081e-02,
            3.34025463208076148213798717279133e-02,
            3.80831534534658497359593809505895e-02,
            4.24969328811189081540611311993416e-02,
            4.66973247315148262681638868798473e-02,
            5.06971977965171571867131206090562e-02,
            5.44186751783839323115543606945721e-02,
            5.78104574976093729676840382580849e-02,
            6.08986802046619438155694581382704e-02,
            6.36956152491011812211141318584851e-02,
            6.61495778159501279791498973281705e-02,
            6.82207062610256376178341497507063e-02,
            6.99297650083991056968457655784732e-02,
            7.12933463637844544447119687902159e-02,
            7.22754822220333659199553721919074e-02,
            7.28456528305081590923819589988852e-02,
            7.30274879627689638139642624992121e-02,
            2.55173329221139791322947587559611e-03, // N = 45
            7.14224577312841824722200456676546e-03,
            1.21547145356169263019641135770144e-02,
            1.69604728123593055666429307848375e-02,
            2.15594944486100330294231497418878e-02,
            2.61058711763036133124415982820210e-02,
            3.06016012229099361452444583164834e-02,
            3.49240004607826656779501206528948e-02,
            3.90270074808360192819556289123284e-02,
            4.29532548651164261532819921285409e-02,
            4.67043249593880327452666278986726e-02,
            5.02194562942364433610897833659692e-02,
            5.34657348412062999321037182198779e-02,
            5.64572978608792325205811835076020e-02,
            5.91911830291232260448097690641589e-02,
            6.16324131388590185087750228376535e-02,
            6.37611302901642529317172147784731e-02,
            6.55826103897497181272058242029743e-02,
            6.70927443324166872251623772172024e-02,
            6.82731235095964533732271206645237e-02,
            6.91161994196663465039875973161543e-02,
            6.96251623651319706542750509470352e-02,
            6.97964470034189016223180601627973e-02,
            2.33998949946640335054159898220405e-03, // N = 47
            6.54685940139563757322882509015471e-03,
            1.11469818828354976653072228032215e-02,
            1.55633574611121414110748162329401e-02,
            1.97915998280810308262989138938792e-02,
            2.39783158613828470406836856909649e-02,
            2.81343907445832583369416113328043e-02,
            3.21435410254925016393379166856903e-02,
            3.59565794576613625976868604539050e-02,
            3.96203136006606088104220475543116e-02,
            4.31469438241565625413720397318684e-02,
            4.64741331712496680284019134887785e-02,
            4.95618239500199495028986973466090e-02,
            5.24323933189405899657486997966771e-02,
            5.50957582046861515934210729028564e-02,
            5.75102602994165407190862993047631e-02,
            5.96442712520207779514080925764574e-02,
            6.15137201590668231121483700007957e-02,
            6.31299044502810074996901334998256e-02,
            6.44629681747904831334849973245582e-02,
            6.54880595317243879849300469686568e-02,
            6.62213047541439503440585667703999e-02,
            6.66780944357798222021926903835265e-02,
            6.68368714221058285440690838186129e-02,
            2.15230855094616100112170364866415e-03, // N = 49
            6.02567101572035624529322106468499e-03,
            1.02597864092800142993278100789212e-02,
            1.43274446308840081726332371658827e-02,
            1.82311785503874168590243698417908e-02,
            2.21040849000614728070424064299004e-02,
            2.59511946613731718513928825586845e-02,
            2.96713060906589227994079038808195e-02,
            3.32273783198292621543501468295290e-02,
            3.66581002422127488760139613077627e-02,
            3.99676238936221978059748494160885e-02,
            4.31059281936955265845945461933297e-02,
            4.60458917765644917818868009362632e-02,
            4.88013867532589573627888057671953e-02,
            5.13719513834576396726916414081643e-02,
            5.37279455017507998060288798569673e-02,
            5.58517151030638800413008482337318e-02,
            5.77486753756895204725552162017266e-02,
            5.94165432459521428154580746650026e-02,
            6.08380348731280343188565495893272e-02,
            6.20040014197816222174530764732481e-02,
            6.29171122696984830291455637052422e-02,
            6.35748787129722797706321557598130e-02,
            6.39696262413755045717067559962743e-02,
            6.41004637692669798632039146468742e-02,
            1.98738389233050127477553381538655e-03, // N = 51
            5.56193213535594640356540807601959e-03,
            9.47397338617417261730224709026515e-03,
            1.32362291955716339375559442714803e-02,
            1.68478177091289232913950968395511e-02,
            2.04353711458829453984087365370215e-02,
            2.40099456069531071167322267001509e-02,
            2.74753175878516067709433912114037e-02,
            3.07923001673870572192370786979154e-02,
            3.40021302743288081349426477117959e-02,
            3.71162714834156332033288094862655e-02,
            4.00838255040327148814860436232266e-02,
            4.28728450201689356702239308560820e-02,
            4.55029130499226830419701173013891e-02,
            4.79825371388375582215601866664656e-02,
            5.02776790807149542850140733207809e-02,
            5.23628858064081187384530835515761e-02,
            5.42511298885454129603544970450457e-02,
            5.59508112204117058485763891440001e-02,
            5.74371163615675431324270050481573e-02,
            5.86896800223938933105394255562715e-02,
            5.97203403241740801710157882098429e-02,
            6.05394553760467968306357988694799e-02,
            6.11285097170536154131958994639717e-02,
            6.14711898714256840814407212292281e-02,
            6.15808180678330818746957220355398e-02,
            1.83981185146107092780176639479350e-03, // N = 53
            5.15173594601833328282536328401875e-03,
            8.77527670729943976013487372256350e-03,
            1.22618158633556548903209559853167e-02,
            1.56152409285371558678168213418758e-02,
            1.89514371450910344696350051663103e-02,
            2.22769735973087114333512914754465e-02,
            2.55069151234083094093030297244695e-02,
            2.86108832572471716293449617296574e-02,
            3.16238591915242867047552977055602e-02,
            3.45513687785811499098009846875357e-02,
            3.73516075433682481765629290748620e-02,
            4.00019941896014447069163111336820e-02,
            4.25158571389079517621745196720440e-02,
            4.48943287753945582951864423648658e-02,
            4.71122199916565870259077541959414e-02,
            4.91541399458680500211826824852324e-02,
            5.10256137066896348075673017774534e-02,
            5.27256963108731838141274295139738e-02,
            5.42387955368089300089984305941471e-02,
            5.55556924442242999750973808659182e-02,
            5.66789557753628603364859372959472e-02,
            5.76069978277142097367047313127841e-02,
            5.83313553537838369589252351943287e-02,
            5.88485769306596878669424199870264e-02,
            5.91603358092347084151718661360064e-02,
            5.92650286600385350910258352996607e-02,
            1.70886049635052121066502994750635e-03, // N = 55
            4.78353655531941167333709330478086e-03,
            8.15078489918117862766955283859716e-03,
            1.13935063444865203319267266124371e-02,
            1.45128827747717601553967270433532e-02,
            1.76192534776518847094983755141584e-02,
            2.07233831861199715995702774762321e-02,
            2.37442938214378687633576703319704e-02,
            2.66500927136609153111912462463806e-02,
            2.94773082453517153156408170389113e-02,
            3.22366327916649847429297892631439e-02,
            3.48857827646454343728521507728146e-02,
            3.73987947325040703816512177581899e-02,
            3.97930352907439194298788720516313e-02,
            4.20760498836970364688880863468512e-02,
            4.42196413088645698397094463416579e-02,
            4.62030328414019669791557021198969e-02,
            4.80372226588824113857612019273802e-02,
            4.97288989532169989349341676643235e-02,
            5.12573120491268130471951280924259e-02,
            5.26056347498077767066426702058379e-02,
            5.37830940251159614340359382822498e-02,
            5.47971549572735597277706176555512e-02,
            5.56319998035080323650625189202401e-02,
            5.62739336119517513656873575200734e-02,
            5.67325818528369094084773394115473e-02,
            5.70173101466441359375103559159470e-02,
            5.71159701275654393959335664021637e-02,
            1.59073604070683626877935612498050e-03, // N = 57
            4.45493629669261887588094239731618e-03,
            7.59080105310381419991827556259523e-03,
            1.06118588421720491665745100817730e-02,
            1.35226653313627164648691447723650e-02,
            1.64248857998400554780715765446075e-02,
            1.93257803768257831189547601979939e-02,
            2.21530233818411602386699854605467e-02,
            2.48812743609629558050322373219387e-02,
            2.75421408387825708552476555723842e-02,
            3.01418139152947912873248270670956e-02,
            3.26448788910208009816926733037690e-02,
            3.50323223518431564604824757225288e-02,
            3.73167750660178890176332799910597e-02,
            3.95003620383103659641221838683123e-02,
            4.15615404229303861405320219546411e-02,
            4.34869654635349350835227255629434e-02,
            4.52821749717779303834319648558449e-02,
            4.69471747435963801531322303617344e-02,
            4.84681238318949852983408277395938e-02,
            4.98363449077796408226426194687519e-02,
            5.10544369656874136298441158032801e-02,
            5.21215342402874121097156034920772e-02,
            5.30292824785586897062827915760863e-02,
            5.37732082090743648827846357107774e-02,
            5.43547798764375811320093134781928e-02,
            5.47728968446952665938276538781793e-02,
            5.50237748090774622666820903305052e-02,
            5.51070152997779061365690722595900e-02,
            1.48503230412374512964257533553791e-03, // N = 59
            4.15774244739312587998414372236766e-03,
            7.08636458790203732638346423300391e-03,
            9.90975355787943393282013460066082e-03,
            1.26302962946196611904170481466281e-02,
            1.53449041737669256840748133186025e-02,
            1.80638261465426892826702243155523e-02,
            2.07179403579355117526183960308117e-02,
            2.32808150168917586675387809691529e-02,
            2.57849773781425942176248611303890e-02,
            2.82403515646854619269845443341183e-02,
            3.06112790420932923129981872989447e-02,
            3.28763049391902831275480423300905e-02,
            3.50509668800313978209715060074814e-02,
            3.71420802022058502145362979263155e-02,
            3.91259797325003780277263842890534e-02,
            4.09854738855193051483283284142090e-02,
            4.27301386748522651903847702214989e-02,
            4.43655707500960894140717982736533e-02,
            4.58742757569110051751870571479230e-02,
            4.72422209376026080995814027119195e-02,
            4.84769417203402067095829863774270e-02,
            4.95841471528194049911419938325707e-02,
            5.05503145288304644999755055323476e-02,
            5.13638822664084990221589066550223e-02,
            5.20321731840021547976782301248022e-02,
            5.25618984127512248183400345169503e-02,
            5.29424463358925470601867857567413e-02,
            5.31642228165634597725208720930823e-02,
            5.32353579030115861558947187859303e-02,
            1.38901369867671297883560121988467e-03, // N = 61
            3.89046112709973872581525888847409e-03,
            6.63070391593134200042269910113646e-03,
            9.27327965951760431473349655107086e-03,
            1.18230152534958520005314852596712e-02,
            1.43697295070457069926517235103347e-02,
            1.69208891890542077740544613106977e-02,
            1.94141411939422747767736154855811e-02,
            2.18280358216083776590199505562850e-02,
            2.41911620780811756348249730308453e-02,
            2.65099548823328583224689936059804e-02,
            2.87540487650424191057307865548864e-02,
            3.09072575623881573569917691202136e-02,
            3.29814470574837995120454081643402e-02,
            3.49793380280609897403643060442846e-02,
            3.68823646518216460843397896951501e-02,
            3.86789456247275467704049844996916e-02,
            4.03745389515359973109376312550012e-02,
            4.19698102151635152323727595558012e-02,
            4.34525397013559924741521456326154e-02,
            4.48148001331629755594754271896818e-02,
            4.60592382710063794060140196506836e-02,
            4.71855465692997064208746849089948e-02,
            4.81858617570871186619463344413816e-02,
            4.90554345550293854905099522056844e-02,
            4.97956834270740222869733315746998e-02,
            5.04059214027822721782001735846279e-02,
            5.08817958987483887067782006852212e-02,
            5.12215478492599324278344852245937e-02,
            5.14261285374583640428447495196451e-02,
            5.14947294294524487989761496464780e-02,
            1.30246271267266404587925610059074e-03, // N = 63
            3.64713272677797805537691644417464e-03,
            6.21744174797783568514608631971896e-03,
            8.69759093344999421881791334953959e-03,
            1.10906494535923660915699429097003e-02,
            1.34823525002951451201571586580030e-02,
            1.58823377570664267532940527871688e-02,
            1.82308870459734727320633140834616e-02,
            2.05057508028605832428592492533426e-02,
            2.27360386405732056713802080594178e-02,
            2.49309353806482711379821637365239e-02,
            2.70599742359002963520975271194402e-02,
            2.91051633767215808812345301248570e-02,
            3.10804943630842364643562802939414e-02,
            3.29921865123988591883552601302654e-02,
            3.48201380392518175521665568794560e-02,
            3.65499425876553082903619440457987e-02,
            3.81900879909417220736678189041413e-02,
            3.97454217782653301815898316817766e-02,
            4.12010625351898612800383148169203e-02,
            4.25451960368526671540934103177278e-02,
            4.37841956551739686087643121936708e-02,
            4.49226469517313778401224055869534e-02,
            4.59489447540288309390632548456779e-02,
            4.68532673005632033236267375286843e-02,
            4.76414364160321207597448278647789e-02,
            4.83185016326540400788402962461987e-02,
            4.88752161616571728641744698506955e-02,
            4.93033500326472071129124685739953e-02,
            4.96090348242765252773089912352589e-02,
            4.97983005161995520571061035752791e-02,
            4.98637171937756085160486918539391e-02,
            1.22336081795172192145104705929270e-03, // N = 65
            3.42681877577254590666600009285503e-03,
            5.84173707916625997715875939775287e-03,
            8.17250403853159342049128355256471e-03,
            1.04239873988075156668875465015844e-02,
            1.26760548066536405525939201766050e-02,
            1.49361036060853651086244298085148e-02,
            1.71498052097839859264638562308392e-02,
            1.92987714303275020855110710726876e-02,
            2.14089131848227767762615769697732e-02,
            2.34866596721624472376976910936719e-02,
            2.55056954808952768276597566909913e-02,
            2.74520984222116105899491600439433e-02,
            2.93369566896209271744666580161720e-02,
            3.11633255619743615438821393581748e-02,
            3.29150776439031400588675069229794e-02,
            3.45821227447337675720007155177882e-02,
            3.61697694756424950601747525524843e-02,
            3.76791306456132485402932275064813e-02,
            3.90994201333069515968965390584344e-02,
            4.04234923703730361643771118451696e-02,
            4.16540199856420406687718127614062e-02,
            4.27911155964466327628059616472456e-02,
            4.38275440301400809328669083697605e-02,
            4.47586387497661830625617085388512e-02,
            4.55858265645481958161511215621431e-02,
            4.63087567380258691152050687378505e-02,
            4.69229682817032256458844585722545e-02,
            4.74260618738824094031691913642135e-02,
            4.78189087369880749811557052453281e-02,
            4.81009691854588014581217692011705e-02,
            4.82701930757775538038956142372626e-02,
            4.83263839865678140883531455074262e-02,
            1.15160129004742220470980385016446e-03, // N = 67
            3.22508952862994927035522607638995e-03,
            5.49895030069660634836070656206175e-03,
            7.69465598754205237080894264067865e-03,
            9.81563482128566117124179868369538e-03,
            1.19382338545769087212455872304417e-02,
            1.40714538620498822579785169750721e-02,
            1.61631626533988541349895484700028e-02,
            1.81943779525545433484179369543199e-02,
            2.01912748960626532712669956026730e-02,
            2.21623428612947974414293383915719e-02,
            2.40812526535429081986361410372410e-02,
            2.59327194192369783753981948848377e-02,
            2.77294076333354858054924818588916e-02,
            2.94770275698765411853674578424034e-02,
            3.11583166083577237093216183438926e-02,
            3.27610610773681476537433354678797e-02,
            3.42928773345582832421385433008254e-02,
            3.57580635550850747805817775315518e-02,
            3.71438479939325688627960175836051e-02,
            3.84401906206052260128736008937267e-02,
            3.96526225681413033163913439693715e-02,
            4.07849728885320908511324944356602e-02,
            4.18272280048631941995473937367933e-02,
            4.27709880050780935634158197444776e-02,
            4.36210523005745795521725938215241e-02,
            4.43813870354051315247900788563129e-02,
            4.50439274744267800776320598288294e-02,
            4.56015770080309551515185262360319e-02,
            4.60591411616620913238584478222037e-02,
            4.64211428552714355788566535920836e-02,
            4.66810091950832992124809095457749e-02,
            4.68326866336052152761659783664072e-02,
            4.68814447905708600594643087333679e-02,
            1.08566449090454430169427890717770e-03, // N = 69
            3.04135509836280524056939533750210e-03,
            5.18554868303459839257163466186284e-03,
            7.25644130761681806218721391132931e-03,
            9.25880912675061326644332382329594e-03,
            1.12640938399336965752839390120243e-02,
            1.32794693467551076088151162934992e-02,
            1.52571615892031220429458926446387e-02,
            1.71812317334183208006326282202281e-02,
            1.90752233953005757849386014868287e-02,
            2.09454147928236564246695650126640e-02,
            2.27687840047177750268936335942271e-02,
            2.45332419916974298068623738799943e-02,
            2.62491191320310575385565954320555e-02,
            2.79196335601209419396973032689857e-02,
            2.95306676104479977340577789846066e-02,
            3.10733839228619912464779417859972e-02,
            3.25528956072243663699694593560707e-02,
            3.39706097099168879971387013938511e-02,
            3.53169823296533499923377519280621e-02,
            3.65856069613536907803030828745250e-02,
            3.77791510382876061235890574607765e-02,
            3.88980364602782499594546550270024e-02,
            3.99356779984855886356243104273744e-02,
            4.08876557940064319640605106087605e-02,
            4.17554190617230938653570149199368e-02,
            4.25388848261954027885067830538901e-02,
            4.32337145652979329413234665935306e-02,
            4.38372568862537143052904298201611e-02,
            4.43503631054797120558674805579358e-02,
            4.47727112312344271982667009979195e-02,
            4.51018669264676708152705941756722e-02,
            4.53368566008377910092619345050480e-02,
            4.54782563462682171140372133777419e-02,
            4.55256218501140716425901189268188e-02,
            1.02550911074644366879904389122657e-03, // N = 71
            2.87226001447005033564985332361630e-03,
            4.89809089031627026972204319577031e-03,
            6.85548721878363482434837195000910e-03,
            8.74803476789708447936000368372333e-03,
            1.06441267608039253494967013580208e-02,
            1.25521386316194451249206309739748e-02,
            1.44261486252934487128918306098058e-02,
            1.62497719998498067750514195495271e-02,
            1.80466511295591033881002829275531e-02,
            1.98246307319263764812333761256014e-02,
            2.15607290028205604570654685403497e-02,
            2.32418108954669105914447868599382e-02,
            2.48793898649795584832045136636225e-02,
            2.64787298392453081252728708250288e-02,
            2.80248592704805711550708480217509e-02,
            2.95073129404832372457700984114126e-02,
            3.09329856908927419700816585645953e-02,
            3.23057496748598085845038951902097e-02,
            3.36145496277944280660854303732776e-02,
            3.48507762898166845166869620697980e-02,
            3.60193210644327230229855274501460e-02,
            3.71234780367496533526328050811571e-02,
            3.81545539384521500969604801412061e-02,
            3.91053151646672883523514485659689e-02,
            3.99798348609348361271109695280757e-02,
            4.07813447585925192839795272448100e-02,
            4.15027911411042157996398316299747e-02,
            4.21380228974243611905770023895457e-02,
            4.26909348444928088417427147760463e-02,
            4.31650461201108504027956769277807e-02,
            4.35545454169717280445972562574752e-02,
            4.38541549245971135073673963233887e-02,
            4.40679834669348430287172391217609e-02,
            4.42000975259000394856911952956580e-02,
            4.42456657210557741111145446666342e-02,
            9.69970723056737650982772613872385e-04, // N = 73
            2.71743687890924024916361467774095e-03,
            4.63395164325241647879094486484064e-03,
            6.48601212092189075703041467590992e-03,
            8.27822898659344268146309531175575e-03,
            1.00748554613388739686907769055324e-02,
            1.18827604423468926458928862643916e-02,
            1.36595943388832276321753766978873e-02,
            1.53914070441378350584393785993598e-02,
            1.70996514888438200241438380544423e-02,
            1.87903735394326400209852323541782e-02,
            2.04432631425704516847652314481820e-02,
            2.20477319276916987333958530825839e-02,
            2.36133900508943110618798044697542e-02,
            2.51435062625416684556345359169427e-02,
            2.66256318015112812547240395133485e-02,
            2.80519817974916041425359480854240e-02,
            2.94274467726939881195846737682587e-02,
            3.07536188420513834085312510069343e-02,
            3.20220215354759460413269778200629e-02,
            3.32269174323257948655552240779798e-02,
            3.43709400346649610047400358325831e-02,
            3.54547340356671514260966660003760e-02,
            3.64723338657418488795158850734879e-02,
            3.74196314217593653528304287192441e-02,
            3.82980935912858380665291235800396e-02,
            3.91078464427406582992752248628676e-02,
            3.98447829980593387633192037355911e-02,
            4.05062091376607799619868899299036e-02,
            4.10929816023217417408908147535840e-02,
            4.16049557991777507748309972157585e-02,
            4.20395629128239925464960435874673e-02,
            4.23954203576963062349847177756601e-02,
            4.26730754760015068560718987100699e-02,
            4.28722419739430843366179146869399e-02,
            4.29917262050515183724463952330552e-02,
            4.30314238248796915309313249053957e-02,
            9.19046467820539762609566292184127e-04, // N = 75
            2.57430114789888560625219504629513e-03,
            4.39053424147683134248776326558072e-03,
            6.14631782634312683749611139205626e-03,
            7.84526932154258616058939423965057e-03,
            9.54898990912019657306686326592171e-03,
            1.12652602088919671224909180295981e-02,
            1.29533087209931594557810186074676e-02,
            1.45988479259487567707420652141082e-02,
            1.62233229017583052700146595270780e-02,
            1.78339863185541201706652003622366e-02,
            1.94106010531388054052293057338829e-02,
            2.09417640401454059617680769633807e-02,
            2.24379827940323905988151409474085e-02,
            2.39041239571709876465810395984590e-02,
            2.53270869762166339622666555442265e-02,
            2.66978178706687406529507455843486e-02,
            2.80225996781889273579135846148347e-02,
            2.93049591842368360727899556650300e-02,
            3.05352495319923672445483475712535e-02,
            3.17060254827262327781411954674695e-02,
            3.28216729927391787091650598995329e-02,
            3.38850902028915296204658602619020e-02,
            3.48886820916981810203338909559534e-02,
            3.58261765004404056367270925420598e-02,
            3.67011100454975106033295162433205e-02,
            3.75161976645481398673354078709963e-02,
            3.82652457003135951230099465192325e-02,
            3.89428943026916274394721995122381e-02,
            3.95523917674562366930679502274870e-02,
            4.00965670518957234547130497048784e-02,
            4.05702759714426930415243077732157e-02,
            4.09688946616749288809344875517127e-02,
            4.12957235315390552843339833088976e-02,
            4.15539208724312394971356354744785e-02,
            4.17391693588452170060598689360631e-02,
            4.18474379306157523439324563696573e-02,
            4.18823075888248921860856910370785e-02,
            8.71830039578744340859894901285543e-04, // N = 77
            2.44262927158914481748364089241932e-03,
            4.16585596178396973254809410036614e-03,
            5.83193947997377986486311485236911e-03,
            7.44528650820709767682581414760534e-03,
            9.06397404052702339305458423268647e-03,
            1.06945277358895321495602104278078e-02,
            1.22991393615884351403488849996393e-02,
            1.38654948950711481847619666041282e-02,
            1.54131994589632136116730265484875e-02,
            1.69480245616357577675969992014871e-02,
            1.84519184755407329723286835587714e-02,
            1.99155342606260228610626228373803e-02,
            2.13478081415702965195624329908242e-02,
            2.27519867911305413710199019305946e-02,
            2.41170183907028386205428915900484e-02,
            2.54360049739543563063204345553459e-02,
            2.67136013970907422454548196810720e-02,
            2.79515074077417366438247370297177e-02,
            2.91421617238904751001626891593332e-02,
            3.02804200572957642190186078323677e-02,
            3.13688591433207222824997018051363e-02,
            3.24082802092718474940014061758120e-02,
            3.33932859263476877753618055066909e-02,
            3.43200950022273312822740365390928e-02,
            3.51901806253909280042257989862264e-02,
            3.60038290706020183695734715456638e-02,
            3.67572089260188861192801823563059e-02,
            3.74476941752304517962990360047115e-02,
            3.80761544360130391173591135611787e-02,
            3.86425885362942089784610288916156e-02,
            3.91444324761338405260779893524159e-02,
            3.95801090552659121102330175290263e-02,
            3.99501607343730053001351620878268e-02,
            4.02544277830611738067112526096025e-02,
            4.04914571212889526363731818037195e-02,
            4.06606738918781976388494570073817e-02,
            4.07624450992558687301148268034012e-02,
            4.07965097073479873723833577514597e-02,
            8.28340760507506579900238730118645e-04, // N = 79
            2.32040070293279294261212797323424e-03,
            3.95792719985567451740360311873701e-03,
            5.54164675245742872899956665833088e-03,
            7.07513035758614017289858111325884e-03,
            8.61413688422363321706143324263394e-03,
            1.01658913604506656591652813403925e-02,
            1.16939421274049413362883242939461e-02,
            1.31857183185855042495404632063583e-02,
            1.46607491797503108194034027178532e-02,
            1.61257467574369671436951279019922e-02,
            1.75627515999212981123722698839629e-02,
            1.89617742220646694206731552867495e-02,
            2.03324376996833061648217721995024e-02,
            2.16792519803111830012376515242067e-02,
            2.29906614889065358253716908620845e-02,
            2.42587643200532984688599924538721e-02,
            2.54893157235800589532903615008763e-02,
            2.66855529271449835870821942762632e-02,
            2.78389946961139084224967632508196e-02,
            2.89431512073271765550508405340224e-02,
            3.00019960385258799284713404631475e-02,
            3.10181220229906497165561773954323e-02,
            3.19848518161208114629623366909073e-02,
            3.28967104059759915535288143928483e-02,
            3.37568236254099721116439525303576e-02,
            3.45675295529186826781753438808664e-02,
            3.53233652633343636617624383688963e-02,
            3.60196353593554910443863548152876e-02,
            3.66591144056713572063621597862948e-02,
            3.72441422807844799147680703299557e-02,
            3.77701545467850965942524510410294e-02,
            3.82330819135516877804725766054617e-02,
            3.86356463038312197832979677514231e-02,
            3.89803717033950364312389069709752e-02,
            3.92633980655014841465444419554842e-02,
            3.94811658198129522556740766958683e-02,
            3.96365421612499824188802222124650e-02,
            3.97323761009928042020611371754057e-02,
            3.97653726949877134311250870268850e-02,
            7.87863323894412892652028279627530e-04, // N = 81
            2.20748573572655207991610737394694e-03,
            3.76522867934218213870067870630010e-03,
            5.27194271488538781372801267366413e-03,
            6.73181348520744595592679715423401e-03,
            8.19757638675165482833318009170398e-03,
            9.67540148401653012089074223922580e-03,
            1.11313216640265694179490196802362e-02,
            1.25543847685168352690254778281087e-02,
            1.39625598669800687207098732756094e-02,
            1.53613263591038558264489921612039e-02,
            1.67345324750035190364272352780972e-02,
            1.80738684088178856723683196605634e-02,
            1.93876458943171882387535021052827e-02,
            2.06790432735283989662544712473391e-02,
            2.19381873358342055491121413979272e-02,
            2.31589310133770848176837375831383e-02,
            2.43456901822737999119272700454530e-02,
            2.55002176031297218827820216802138e-02,
            2.66157374990245755574935770937373e-02,
            2.76876261110605252635519235582251e-02,
            2.87183868410914207303097356316357e-02,
            2.97089272777770613265246879564074e-02,
            3.06543608914110025931432090828821e-02,
            3.15512236191161504761382161632355e-02,
            3.24009825076053761816474718671088e-02,
            3.32040443412578642479182633451273e-02,
            3.39568628342087827642892250423756e-02,
            3.46569358434978061489495360092405e-02,
            3.53051447086217343174219251977775e-02,
            3.59016027836281254037587018501654e-02,
            3.64438265303401107142455828125094e-02,
            3.69301695340484223417654163768020e-02,
            3.73611800254688292133309346354508e-02,
            3.77368012630936722207053435340640e-02,
            3.80554637788527092001622520456294e-02,
            3.83163240051739087399518268739484e-02,
            3.85197417499504937699050799437828e-02,
            3.86655554391414288395445453261345e-02,
            3.87530293787521837312048944568232e-02,
            3.87821047642838354074790174763621e-02,
            7.50429320820811046263698607106107e-04, // N = 83
            2.10228358929712274769108226735170e-03,
            3.58621484585954029139509557921883e-03,
            5.02192668922512089335619123176002e-03,
            6.41289622624138973272511776713145e-03,
            7.80982310440631651710097216323447e-03,
            9.21941893246768819081271573168124e-03,
            1.06088920583386186330399070243402e-02,
            1.19670940382880144209343242778232e-02,
            1.33118755979416379664481695499489e-02,
            1.46494567490795292441507768899100e-02,
            1.59637886319773589227644094989955e-02,
            1.72460491044326529042063356200742e-02,
            1.85050797107342429592691246398317e-02,
            1.97450684633009715396312344637408e-02,
            2.09557486858472780122397693958192e-02,
            2.21301689763428871549066911939008e-02,
            2.32736234908143199695551572858676e-02,
            2.43891006082099515150929391893442e-02,
            2.54690919863180299798077754758197e-02,
            2.65078988129795987960246606007786e-02,
            2.75091495122560501795927478951853e-02,
            2.84751929771580730710311968323367e-02,
            2.94001228729363767167015453196655e-02,
            3.02791292235336691185398905190596e-02,
            3.11150132077961695531431729477845e-02,
            3.19098287082358739175091955075914e-02,
            3.26587344403081389354603913943720e-02,
            3.33575951739588441591344292191934e-02,
            3.40088278201884641749330739912693e-02,
            3.46144155702144129538311290161801e-02,
            3.51702958963641329481752961783059e-02,
            3.56728717226359182124184599160799e-02,
            3.61244401151421812290465140904416e-02,
            3.65270705771046921839229071338195e-02,
            3.68773068051132940636804846690211e-02,
            3.71719913379935235075990362929588e-02,
            3.74134748786695003897051492458559e-02,
            3.76040317405194959854419778366719e-02,
            3.77406930826910957943454150154139e-02,
            3.78206578048135774738902625813353e-02,
            3.78464538188871546520175570549327e-02,
            7.15467085805285740902903501847732e-04, // N = 85
            2.00472607890585024711938011421353e-03,
            3.41970626170950975364348778384738e-03,
            4.78882487864555183437742513774538e-03,
            6.11604246466967982343021503766067e-03,
            7.44944624579055997282139855997229e-03,
            8.79485362349846991336654866699973e-03,
            1.01215761169300231397949474398956e-02,
            1.14198071629799825094098153499544e-02,
            1.27060638110606544809444429233736e-02,
            1.39855304404149002189816641816833e-02,
            1.52436686048831124967728456454097e-02,
            1.64730429295141117540524078322051e-02,
            1.76813899779599131845131410045724e-02,
            1.88717912456202799309501472180273e-02,
            2.00353755789132344233838267655301e-02,
            2.11666351695655105547011487487907e-02,
            2.22697501233139333320920627556916e-02,
            2.33464879538915447143576642474727e-02,
            2.43907490429229739659078290969774e-02,
            2.53983645346068133419326073862976e-02,
            2.63717534092876501605751116130705e-02,
            2.73118919361154607883257483535999e-02,
            2.82143480656886803947802633274478e-02,
            2.90759540779039135638406321504590e-02,
            2.98981597074336122310533880863659e-02,
            3.06814605059700824807311647646202e-02,
            3.14225871220973618225258405800560e-02,
            3.21191860976889481671392445605306e-02,
            3.27721456785988810023191319942271e-02,
            3.33816694117022028098773489546147e-02,
            3.39453928788535155836036949494883e-02,
            3.44616733261326538273472408491216e-02,
            3.49310680053013938861639076094434e-02,
            3.53536040512073476693721829633432e-02,
            3.57276815866811731092766990514065e-02,
            3.60523130644657963106425313526415e-02,
            3.63278603059973143052374666694959e-02,
            3.65542409672942117393468208774721e-02,
            3.67305413863710447652799473416962e-02,
            3.68564040020365121796963592259999e-02,
            3.69320725127922286357140535528742e-02,
            3.69573851375539982888618339984532e-02,
            6.83014409444813791125183932706477e-04, // N = 87
            1.91352970506636138256495449638805e-03,
            3.26448731385196215873389924411185e-03,
            4.57197215965471012721899057851260e-03,
            5.83933975749266996613240365832098e-03,
            7.11288144376080559705410877313625e-03,
            8.39883736760512096541919646597307e-03,
            9.66754483943707901283382000201527e-03,
            1.09090470052662421446276752590165e-02,
            1.21397171508674378559433648661070e-02,
            1.33653282186976807288658619654598e-02,
            1.45714496319469446333760842549054e-02,
            1.57502335708427990135227503287751e-02,
            1.69098279309978505313694085998577e-02,
            1.80541291607646606220960450173152e-02,
            1.91739560289897227607358587420094e-02,
            2.02631490603018930840573119667170e-02,
            2.13265957410324960563663410084700e-02,
            2.23670667107838463949498475358268e-02,
            2.33778723066415776432602768863944e-02,
            2.43539740944365146191330495639704e-02,
            2.52987057545335410069231585339367e-02,
            2.62142153588320742096939852672222e-02,
            2.70952482125000997104091737810450e-02,
            2.79375527135172704862320358643046e-02,
            2.87436662944730685065319875093337e-02,
            2.95154217742633132037788357138197e-02,
            3.02485081805798951271047059208286e-02,
            3.09392646059463184704529936652762e-02,
            3.15898303301099386830586013275024e-02,
            3.22019211811579442183983701397665e-02,
            3.27719086922384494897642071009614e-02,
            3.32965992993431922353231300348853e-02,
            3.37779701913215324449168974751956e-02,
            3.42177572733837961904690416758967e-02,
            3.46128591168387289567220932440250e-02,
            3.49604635767021970638168681944080e-02,
            3.52625393246283128090290404088591e-02,
            3.55209439395506657022316687744024e-02,
            3.57329991487812179129512912822975e-02,
            3.58962058048124116327315391572483e-02,
            3.60126320686600803755439414999273e-02,
            3.60843383740518872104807712730690e-02,
            3.61089903517822843892481898819824e-02,
            6.52609239669610613314432168152734e-04, // N = 89
            1.82866662312671304779776448867779e-03,
            3.11963151271295920791137845640151e-03,
            4.36914294179755868102743576741886e-03,
            5.58094000187005744029189457933171e-03,
            6.79904203010949902824533452871947e-03,
            8.02892548576001306714911009976277e-03,
            9.24272339819595147025754755532034e-03,
            1.04316020380666729661101044257521e-02,
            1.16107862439096629764145873764392e-02,
            1.27851713787794172422218608176081e-02,
            1.39416004820396635666135409792332e-02,
            1.50733817093048685920031459772872e-02,
            1.61877238133181465540300081329406e-02,
            1.72875948436387871787189851602307e-02,
            1.83649818414824868295642801285794e-02,
            1.94149243967382048592362764338759e-02,
            2.04413742261562551838505186196926e-02,
            2.14460870609502682326841238591442e-02,
            2.24235475869847371288567927649638e-02,
            2.33699841659307551433588656664142e-02,
            2.42877246620108351582434380588893e-02,
            2.51777859133709806804812814107208e-02,
            2.60361382845751762604713519522193e-02,
            2.68598852030172072224978307986021e-02,
            2.76504499909962717096867379495961e-02,
            2.84083918817896255437638330931804e-02,
            2.91307017028212891784910709702672e-02,
            2.98151821571169158009428912237126e-02,
            3.04627224781950436960364925198519e-02,
            3.10735961751540008812799698034723e-02,
            3.16455750815045205870390532254532e-02,
            3.21770615260243697530739837020519e-02,
            3.26686211404204132624506939919229e-02,
            3.31203489644073603703766650596663e-02,
            3.35306657372060334942887038778281e-02,
            3.38985174843230638308533286817692e-02,
            3.42242721444562039700976185940817e-02,
            3.45079117379547203880996164571116e-02,
            3.47484304960003417828140470646758e-02,
            3.49452891969027831797767191801540e-02,
            3.50987332775636734494284496577166e-02,
            3.52086668839763292093714142083627e-02,
            3.52746151705842295176474010531820e-02,
            3.52965433781745607788593588338699e-02,
            6.24291857182897379045793950780308e-04, // N = 91
            1.74909651748554237880861617071560e-03,
            2.98417191546624738576753976815326e-03,
            4.17984253266521534053712372269729e-03,
            5.33932741808157765306397379845293e-03,
            6.50505471381713704093208150425198e-03,
            7.68283318432196743463791221984138e-03,
            8.84569677730070828836073104639581e-03,
            9.98469672095886155716026877371405e-03,
            1.11149000844716055319549852242744e-02,
            1.22416738114025872713463982677240e-02,
            1.33519700688588816017698945870507e-02,
            1.44387621659281071423430731215376e-02,
            1.55095798910579157209310707798977e-02,
            1.65680549706382421182304653939354e-02,
            1.76059282334919929569050367490490e-02,
            1.86177060256254127412756105286462e-02,
            1.96079145136814521344081896359057e-02,
            2.05791313174339962621672839304665e-02,
            2.15253610497680575308621087060601e-02,
            2.24421209931162310424745953696402e-02,
            2.33324891507515723432231169454099e-02,
            2.41984441723208584806847909476346e-02,
            2.50352854772741412192615939602547e-02,
            2.58392332899758658815159151345142e-02,
            2.66126057045400245260058369467515e-02,
            2.73570586993094229388834293104082e-02,
            2.80687353777391221387738085013552e-02,
            2.87443783519136901449808618735915e-02,
            2.93859058381667412329640853840829e-02,
            2.99948279904526486638882687429941e-02,
            3.05678919944721502743867347362539e-02,
            3.11022503108643218194817592348045e-02,
            3.15996335417294063607762666379131e-02,
            3.20615270348692388280298359859444e-02,
            3.24851405886130914502096800333675e-02,
            3.28679599954718945631348958613671e-02,
            3.32116653448070800469515972963563e-02,
            3.35178056108507357868653286914196e-02,
            3.37839606270188136383225696590671e-02,
            3.40078912750661072061930667587148e-02,
            3.41913225869242831667094151271158e-02,
            3.43359362733218348440189515713428e-02,
            3.44396142526863374699885866903060e-02,
            3.45003417525124450593310143631243e-02,
            3.45199599911868298951489464343467e-02,
            5.97684967573795951877035914634462e-04, // N = 93
            1.67481784665280742686876980229727e-03,
            2.85737287489860446870748589276445e-03,
            4.00226648687370106100003042115532e-03,
            5.11302445937321901892058662042473e-03,
            6.23008715205487176996834719489016e-03,
            7.35860658178920639532760716861048e-03,
            8.47316188178166840305749474282493e-03,
            9.56575253679172420040455193657181e-03,
            1.06504500408590233040406758391327e-02,
            1.17318719141599886457427714958612e-02,
            1.27980532271761669738108224692041e-02,
            1.38429393314047043117565038983230e-02,
            1.48732556066118511844953431477734e-02,
            1.58918480543355881973166532361574e-02,
            1.68914437747765648623055056987141e-02,
            1.78675538554650091549458323925137e-02,
            1.88239115205497999083750215731925e-02,
            1.97622425881105352740707559178190e-02,
            2.06775388971262852333410364735755e-02,
            2.15663760475398903759813862279771e-02,
            2.24309874464064494536952309999833e-02,
            2.32724096628488842652959789347733e-02,
            2.40869687772391309621422550435454e-02,
            2.48720134761777275644867302162311e-02,
            2.56289337266913212765029328465971e-02,
            2.63583327910462995868901003859719e-02,
            2.70574413972946813122799625261905e-02,
            2.77242163581443122610803442285032e-02,
            2.83595421252021591407288525488184e-02,
            2.89637455436348445481087310326984e-02,
            2.95347393935718287305558504840519e-02,
            3.00709935046277812564774478687468e-02,
            3.05730794046400675134655955389462e-02,
            3.10411465983298183457517183114760e-02,
            3.14736658599958779580774148598721e-02,
            3.18695649487714324776810315142939e-02,
            3.22292189517152868893923312043626e-02,
            3.25526625041441947105980148080562e-02,
            3.28388523306812965540935067565442e-02,
            3.30871434458519381172081352815439e-02,
            3.32977861301501157353932569549215e-02,
            3.34707369892656356191729116744682e-02,
            3.36053965903812049131893502362800e-02,
            3.37015328101193389898071472998708e-02,
            3.37593131525360870548446712291479e-02,
            3.37786328692505979920390757342830e-02,
            5.72829097876508940706541395115892e-04, // N = 95
            1.60497905815551087337078595140838e-03,
            2.73845730772187285345653506851704e-03,
            3.83604480111798080629870177915564e-03,
            4.90081757383967978741745596948931e-03,
            5.97180029668951343341243287454745e-03,
            7.05440772856855136119236249214737e-03,
            8.12401483719167941122130116582412e-03,
            9.17253328779174190166223468168027e-03,
            1.02138704414025029837409519473113e-02,
            1.12530244456118411894296471587040e-02,
            1.22781383591508072572473508898838e-02,
            1.32828836421370020948184986764318e-02,
            1.42742372608193092420325598368436e-02,
            1.52555900985343467768373670878645e-02,
            1.62194725139671695746113044833692e-02,
            1.71609553687083887796305248230055e-02,
            1.80842419026828564454500991587338e-02,
            1.89917369831594622098247526764681e-02,
            1.98780383270258063921342994717634e-02,
            2.07391343915472731174176601598447e-02,
            2.15778786449664188029640143895449e-02,
            2.23961039599647956932493286785757e-02,
            2.31895838033569084979390595435689e-02,
            2.39549396073645559646081437676912e-02,
            2.46943034508163294926674780072062e-02,
            2.54091862980178433140121541100598e-02,
            2.60961216921010222269394773775275e-02,
            2.67521972010912149897432499301431e-02,
            2.73791509492214008014698833903822e-02,
            2.79783309851037095827841483242082e-02,
            2.85468102111126192932388789813558e-02,
            2.90820389037249327213174865391920e-02,
            2.95855533122951590285776291011643e-02,
            3.00586464349271269280716722960278e-02,
            3.04988008629325860199266173822252e-02,
            3.09037604143260723199571060604285e-02,
            3.12749827594418494669525898643769e-02,
            3.16137837632046794777984644042590e-02,
            3.19179720704921635054951423171588e-02,
            3.21855341273307241078960316826851e-02,
            3.24179341623930181159884966746176e-02,
            3.26165707709662258673155577071157e-02,
            3.27795190150783621874097661930136e-02,
            3.29049658280787735153971595991607e-02,
            3.29944447353025666069825660997594e-02,
            3.30494862372945411022051587224269e-02,
            3.30683841507867434805767459238268e-02,
            5.49413282427096472983196751016521e-04, // N = 97
            1.53959552984370877729003446177103e-03,
            2.62683534109881986970402856229612e-03,
            3.67970049756695134074435671323045e-03,
            4.70151400816572022367534344766682e-03,
            5.72955182652640660628806656973211e-03,
            6.76866032980113791622800434311102e-03,
            7.79555351944573229200363684299191e-03,
            8.80295005812674162537501132419493e-03,
            9.80388895764546138000827824043881e-03,
            1.08027238623195978584057286298048e-02,
            1.17885255864751004734047867827940e-02,
            1.27557895092654683538713200618986e-02,
            1.37107987316064695859640920616584e-02,
            1.46562739456828142192712505220697e-02,
            1.55855845622811482742431365977609e-02,
            1.64946501366945164068766871423577e-02,
            1.73869966697634305285991018763525e-02,
            1.82643079635756953871261742960996e-02,
            1.91220180797116584558992258280341e-02,
            1.99570068622041546513301568666066e-02,
            2.07714123931758871954844636320558e-02,
            2.15662756387350364184474216244780e-02,
            2.23382371948743531364645065195873e-02,
            2.30848662203849037954928036242563e-02,
            2.38075143310232280324800768767091e-02,
            2.45068135293130227869706772025893e-02,
            2.51802133721940948896111933663633e-02,
            2.58258177135411888525329260346552e-02,
            2.64445011553372938406525349819276e-02,
            2.70366303443647787441150853737781e-02,
            2.76002566622617941105577443750008e-02,
            2.81339283397896364191659301923210e-02,
            2.86382196330264363060003063310432e-02,
            2.91133232289075873089334578480702e-02,
            2.95577759324559749543048781106336e-02,
            2.99705168403725935588610695958778e-02,
            3.03519274946024396333310590989640e-02,
            3.07020854917752043788947702296355e-02,
            3.10199445653509889297971824362321e-02,
            3.13048034688244436463122610803111e-02,
            3.15569185173944152800196150110423e-02,
            3.17762889143052076890150203780649e-02,
            3.19622443006865250558767854727193e-02,
            3.21144264228078180067882385628764e-02,
            3.22330079434589994447080130157701e-02,
            3.23179296153411899084062497422565e-02,
            3.23688730441163419193628669745522e-02,
            3.23858168627014497698013428816921e-02,
            5.27476968378448856505924524640250e-04, // N = 99
            1.47796392817401583442971091386653e-03,
            2.52187657314923482226864948074763e-03,
            3.53295570148335269164419081278083e-03,
            4.51413316260013304515030796437713e-03,
            5.50142039933779799371071916880283e-03,
            6.49987253216620722295893131104094e-03,
            7.48691027641318167240580550014784e-03,
            8.45518563977508755269418827538175e-03,
            9.41757222968566017062830297845721e-03,
            1.03787329241164811427511338592922e-02,
            1.13278438578784945711674936319469e-02,
            1.22591748799479142995050295894544e-02,
            1.31792068212073232302827818784863e-02,
            1.40911110472703472729083529202398e-02,
            1.49880989346804997103257406365628e-02,
            1.58657236988720695691768014512490e-02,
            1.67278985537773657032989405024637e-02,
            1.75768726412449984020103244120037e-02,
            1.84077538519827818563889820779877e-02,
            1.92169329826558238361045027886576e-02,
            2.00070643859270071163170001682374e-02,
            2.07798535198554165659423631495883e-02,
            2.15314818077819852826237934095843e-02,
            2.22589139301300892315182977654331e-02,
            2.29641216311695130214420856873403e-02,
            2.36484943738632588661197075907694e-02,
            2.43089029298124773004197152204142e-02,
            2.49427312116374186312661720421602e-02,
            2.55515676298999211413232046652411e-02,
            2.61366295727179995256328481900709e-02,
            2.66952731071584993538525765188751e-02,
            2.72252058087953593967789345242636e-02,
            2.77278075508690588502069829246466e-02,
            2.82042205700282801184020087248427e-02,
            2.86521667109021771491228491868242e-02,
            2.90696140121513013632181809953181e-02,
            2.94578454056429669960515127513645e-02,
            2.98179973237099396610183532629890e-02,
            3.01480810667995972884636302069339e-02,
            3.04462797396853959708273862361239e-02,
            3.07138558577389579606897740404747e-02,
            3.09519926155660748956499617179361e-02,
            3.11589374965972366882116517672330e-02,
            3.13330525912319732273481065476517e-02,
            3.14756358269987560061231590680109e-02,
            3.15879594586861711658087870091549e-02,
            3.16684660566114092872247454124590e-02,
            3.17156645039733814384064203295566e-02,
            3.17309313985214072606488855399220e-02,
            5.06761668035003286919559783996192e-04, // N = 101
            1.42011023816578920916930961482194e-03,
            2.42310374582142351931879353799104e-03,
            3.39459089289617177778723977610298e-03,
            4.33770360526359102792959276939655e-03,
            5.28690708431084430835023013628415e-03,
            6.24676165289294801907793441841932e-03,
            7.19585591375769551003571677938453e-03,
            8.12753366255909368010001969651057e-03,
            9.05390685313328495709139787095410e-03,
            9.97908051277203618500966086912740e-03,
            1.08930311491453272326745960185690e-02,
            1.17907321005433739224965705716386e-02,
            1.26780618370114523535407968779509e-02,
            1.35576160115580858500639038766167e-02,
            1.44233248722898995536345623236230e-02,
            1.52714638121734802567175393051002e-02,
            1.61053634782937077352116261863557e-02,
            1.69266578757386911002758012045888e-02,
            1.77311684667018631955670571187511e-02,
            1.85160424617774148348114948703369e-02,
            1.92833235218073315020426150567801e-02,
            2.00340458307194310694221428548190e-02,
            2.07651284717193032602899904759397e-02,
            2.14743382018096930219375195747489e-02,
            2.21629849266008066566158163368527e-02,
            2.28317175688748479067680108300920e-02,
            2.34781840789095759547411290668606e-02,
            2.41006258772179897398313386247537e-02,
            2.46999035373259012704494352874462e-02,
            2.52764125748327281306693237183936e-02,
            2.58283368091226477047950282894817e-02,
            2.63543068186906682959236292163041e-02,
            2.68548963629062706348626932140178e-02,
            2.73303318901101099935857519085403e-02,
            2.77792238924391733656538150398774e-02,
            2.82005405794783677031478674734899e-02,
            2.85946683834066468776757830028146e-02,
            2.89617197905012967173998816861058e-02,
            2.93006670351198122981273286313808e-02,
            2.96107849404606930654448859741024e-02,
            2.98923358170391541277499669604367e-02,
            3.01453537745721283913624688466371e-02,
            3.03691332001646135951844485134643e-02,
            3.05632377063106766557076809931459e-02,
            3.07278456694170497287554866261416e-02,
            3.08629341217089812887675037700319e-02,
            3.09680956236687426885723084524216e-02,
            3.10431739969451274407941099298114e-02,
            3.10882877824048831083558752652607e-02,
            3.11033666417499451983808000932186e-02,
            4.87304999364339202442414356042377e-04, // N = 103
            1.36544874278114909682546596059183e-03,
            2.33000101504979425723340646925408e-03,
            3.26439686591731541981387110240576e-03,
            4.17142620889466436695514062193979e-03,
            5.08442054529746612079321721466840e-03,
            6.00810667526670109939157526923736e-03,
            6.92170379743429608349059023453265e-03,
            7.81850559964216394737146487159407e-03,
            8.71046071554973724837545034915820e-03,
            9.60192687508169134824598245359084e-03,
            1.04829822954283138208841918981307e-02,
            1.13484134998613310496562434082080e-02,
            1.22042546136597804262713395928586e-02,
            1.30534765769616117880858041644387e-02,
            1.38898821603156662207734228786649e-02,
            1.47094397009207931287244619511512e-02,
            1.55158008495526258951890952175745e-02,
            1.63110735961609527866489344205547e-02,
            1.70908075092283534557324742308992e-02,
            1.78517392463072542552193766596247e-02,
            1.85963452026383369020123836889979e-02,
            1.93262180774479153111400364650763e-02,
            2.00378923852116766490816246459872e-02,
            2.07286281998831957429363370692954e-02,
            2.14002572074576749572294431800401e-02,
            2.20540651816187628642129681111328e-02,
            2.26872155004254998089674444372577e-02,
            2.32973479088205807918665612987752e-02,
            2.38859241386193341116772614896036e-02,
            2.44540540935250724774441266617941e-02,
            2.49993407798070887970709463843377e-02,
            2.55197149350083161978286483417833e-02,
            2.60164282047372456829759101992749e-02,
            2.64905023258958892407033403060268e-02,
            2.69398692856771919401648318626030e-02,
            2.73626926097259963455154974099059e-02,
            2.77601154404415600973621280900261e-02,
            2.81331335941108623410755740223976e-02,
            2.84799378615283420301818040343278e-02,
            2.87988834796081318023741602019072e-02,
            2.90910743327394555324261204987124e-02,
            2.93575269882304958068974798379713e-02,
            2.95966428135477736816039140421708e-02,
            2.98069371187293062630541129465200e-02,
            2.99895246374859078541952328578191e-02,
            3.01454796444084321960232841774996e-02,
            3.02733778891073959660396042181674e-02,
            3.03718677577939841216725369577034e-02,
            3.04421131727412100365093294840335e-02,
            3.04852771810882154646105135498146e-02,
            3.05000799265303483565059394777563e-02,
            4.68890412532647817694941849708812e-04, // N = 105
            1.31401177344744424062283894016900e-03,
            2.24217902861296742439423113069097e-03,
            3.14135858114051322656501419317010e-03,
            4.01450330166162015765873860573265e-03,
            4.89357103356846158404014346388067e-03,
            5.78285549480728969934384409157246e-03,
            6.66260052647352999516394689294430e-03,
            7.52669680988031237350854851797521e-03,
            8.38642143571117007483373129161919e-03,
            9.24564642367758926511100980860647e-03,
            1.00951448880688358228363554758289e-02,
            1.09303080645236048995538880035383e-02,
            1.17566440766198408024445498654131e-02,
            1.25766261025257782696362696128745e-02,
            1.33846768435568388294631958501668e-02,
            1.41773833343292691294701413085022e-02,
            1.49578928259961208696582346533432e-02,
            1.57277848399199025875017099451725e-02,
            1.64832217695500757304039041173382e-02,
            1.72215865726433534077521869676275e-02,
            1.79448306232038203023027023164104e-02,
            1.86539732755886776549569816552321e-02,
            1.93461807334540242253595465626859e-02,
            2.00193966775023858561954881452039e-02,
            2.06748872641002549854771785931007e-02,
            2.13133092548962732593054170138203e-02,
            2.19324898926281479372146776540831e-02,
            2.25307977860183597518251019664604e-02,
            2.31090761942293887454269452064182e-02,
            2.36677407273614449911836032924839e-02,
            2.42050995837327191650967250780013e-02,
            2.47198654939469256164308319512202e-02,
            2.52126087546057850441449943446059e-02,
            2.56835817560204203446883042261106e-02,
            2.61314711855362737102925763110761e-02,
            2.65552845576970258933968693781935e-02,
            2.69554112786925467726284466607467e-02,
            2.73319919344256617721455882019654e-02,
            2.76840302548599162535403195306571e-02,
            2.80107981542931303020615985133190e-02,
            2.83125631747852650466068524792718e-02,
            2.85893880912908293634444589770283e-02,
            2.88405556942007770815372680317523e-02,
            2.90655840023386971560093172683992e-02,
            2.92646570346388849859220471216759e-02,
            2.94377813146978681291265900199505e-02,
            2.95844950874515726091384948404084e-02,
            2.97045524573255476097344285335566e-02,
            2.97980781089354634927346410222526e-02,
            2.98650341454565829146794442294777e-02,
            2.99052001262343561394096980166069e-02,
            2.99185624812038503117506138551107e-02,
            4.51553309690733660746592148527156e-04, // N = 107
            1.26530785343076336221801447834423e-03,
            2.15921230854912828481251274581609e-03,
            3.02531841217637065613588198687012e-03,
            3.86627851607895464680630936982197e-03,
            4.71303044511106172115288970303482e-03,
            5.57000106329473294169973840439525e-03,
            6.41799937477051038459130438695865e-03,
            7.25087895074616548690693562662091e-03,
            8.07975781197234170505350192570404e-03,
            8.90871556022121251217082971152195e-03,
            9.72862286059749531430540514520544e-03,
            1.05347153795185971558723281304992e-02,
            1.13326238067258493191769019858839e-02,
            1.21251357806568139247049842310844e-02,
            1.29065708397862050071935868800210e-02,
            1.36732569668983061639266907150159e-02,
            1.44286090602558526169163499730530e-02,
            1.51746066083601870849717485612018e-02,
            1.59071838709435829650740146234966e-02,
            1.66233766851126944785743688726143e-02,
            1.73255013842881742947010792477158e-02,
            1.80150498883290891005692913040548e-02,
            1.86888639929835911890343425056926e-02,
            1.93444594182588837372183121487978e-02,
            1.99835441514096164017377788013619e-02,
            2.06073140941819381299904279103430e-02,
            2.12131876782280688609194641003342e-02,
            2.17990265723951720522322261786030e-02,
            2.23661836713129648368525437263088e-02,
            2.29156788265721216013570682434874e-02,
            2.34453311252252327712142232485348e-02,
            2.39532656229841066364283364009680e-02,
            2.44406269940015581643155684332669e-02,
            2.49083388857638081403944596559086e-02,
            2.53545182345186401184911062500760e-02,
            2.57774995610442307636400727233195e-02,
            2.61783122575080344496267770182385e-02,
            2.65578400478954645969054126908304e-02,
            2.69144328127892337731985605842056e-02,
            2.72465969621118221655198254893548e-02,
            2.75553096322739554668856953867362e-02,
            2.78414564425344748799240335301874e-02,
            2.81035761152278289187744775290412e-02,
            2.83403186910750094773536744696685e-02,
            2.85526543486100820024020663367992e-02,
            2.87415032954145312216187591047856e-02,
            2.89055606864295280833410117793392e-02,
            2.90435969416686888544543165835421e-02,
            2.91566095980958922551096179631713e-02,
            2.92455804105937709758133991044815e-02,
            2.93093349655318205493337302414147e-02,
            2.93467429255595164960812581966820e-02,
            2.93588566005714667050963129213415e-02,
            4.35110966080865207809835748520300e-04, // N = 109
            1.21937278348611239341126033508544e-03,
            2.08078078058774153594190359228833e-03,
            2.91542524966249263704276550868144e-03,
            3.72609189131934250352462534294773e-03,
            4.54249285080746308118637699635656e-03,
            5.36867401571611019966967504046806e-03,
            6.18634824193941418313258395755838e-03,
            6.98988746239648326558091540050555e-03,
            7.78981475496990250634299357557211e-03,
            8.58978451265931738922709826056234e-03,
            9.38127427684858072876039614129695e-03,
            1.01600427506467558963487718415308e-02,
            1.09312588153440710253549994490641e-02,
            1.16972771848123414939468744933038e-02,
            1.24529552338060768568173131143340e-02,
            1.31951543139994745962306765818539e-02,
            1.39268499962953689469413731671921e-02,
            1.46495648399596299638059093695119e-02,
            1.53597626103089482385577468903648e-02,
            1.60550348684188014247720133198527e-02,
            1.67372436594253465313997253360867e-02,
            1.74073878188885748652392493340813e-02,
            1.80628534085319411572889691797172e-02,
            1.87017425701202430476932647707144e-02,
            1.93252767050864811271271292980600e-02,
            1.99341134851707645070373331463998e-02,
            2.05262419687796578149363568854824e-02,
            2.11001475195162664644232819455283e-02,
            2.16566536092034286897778372349421e-02,
            2.21961889406663212542802909865713e-02,
            2.27171772786052099390996517058738e-02,
            2.32184109114097064763271305309900e-02,
            2.37004541036327232017555388665642e-02,
            2.41635787338281317337962406099905e-02,
            2.46065470625421445216574056757963e-02,
            2.50284112321297949610432453937392e-02,
            2.54295616580526538663686864083502e-02,
            2.58101613110101532622131514926878e-02,
            2.61692528500437580907256318596410e-02,
            2.65061187838481378264976484615545e-02,
            2.68210307458623467558034292324010e-02,
            2.71140749954542764621479022935091e-02,
            2.73845382884497154374336957971536e-02,
            2.76319151680443908514206441395800e-02,
            2.78563947899993120949080349646465e-02,
            2.80580079008002393481380210005227e-02,
            2.82362623629186307305793945943151e-02,
            2.83908539447119030729727029438436e-02,
            2.85219130068849746617587470609578e-02,
            2.86294276249504583975458160693961e-02,
            2.87131124484366201388141348616045e-02,
            2.87728591594232224748495241328783e-02,
            2.88087537695146077287855490567381e-02,
            2.88207475679800907697458711709260e-02,
            4.19596408108236331498813731499808e-04, // N = 111
            1.17579127342019753958701766549666e-03,
            2.00653090914678679246296866267585e-03,
            2.81156047295043429873340201652354e-03,
            3.59340038641513693368212400969242e-03,
            4.38084198612032765796087119269941e-03,
            5.17803784244214200527256508621576e-03,
            5.96720939332967027779464075365468e-03,
            6.74270170968126365818040568456126e-03,
            7.51488439837821181610522103255789e-03,
            8.28758315713630164256464638583566e-03,
            9.05236863927878949998007129806865e-03,
            9.80486938298080236420251054596520e-03,
            1.05503506587694591278836497849625e-02,
            1.12914321845241603925469320302000e-02,
            1.20228876577233596140148463859987e-02,
            1.27413585722091892565854820418281e-02,
            1.34500448351212876368920845493449e-02,
            1.41508085326335214526594086237310e-02,
            1.48399208761505526504853591518440e-02,
            1.55146780276252480718079951316213e-02,
            1.61772515941589582755266718550047e-02,
            1.68290427088716651460309492449596e-02,
            1.74671619803365811562922971234002e-02,
            1.80893475667000883100321573238034e-02,
            1.86971972097750467611820823776725e-02,
            1.92918278970221589163624997809166e-02,
            1.98708813839717432503384486608411e-02,
            2.04324127548036922619179023286051e-02,
            2.09776801637053846028013737168294e-02,
            2.15076267814876681550018133748381e-02,
            2.20202614459384937717345565033611e-02,
            2.25138790831208024378895515837939e-02,
            2.29895337377514531740363423750750e-02,
            2.34480678479211043785390700122662e-02,
            2.38877615203779009034334990246862e-02,
            2.43070993404254018233068279641884e-02,
            2.47070166596951787396641009308951e-02,
            2.50883063927027985529072395820549e-02,
            2.54494596097490956287945351732560e-02,
            2.57891158987605569052892207082550e-02,
            2.61081495823131636002667477214345e-02,
            2.64073418128670835136606598325670e-02,
            2.66853539795080911545266388884556e-02,
            2.69409550746184563163598824075962e-02,
            2.71749995965336749170759844673739e-02,
            2.73882861514089734344956639233715e-02,
            2.75796170527947935580126426202696e-02,
            2.77478702380414936345953691443356e-02,
            2.78939113457810777818579595077608e-02,
            2.80185801656523507385809779179908e-02,
            2.81207969531590586120817221171819e-02,
            2.81995307047123340560279558530965e-02,
            2.82556826334946949164095286732845e-02,
            2.82901540486563025933453019433728e-02,
            2.83019635580757829285136750741003e-02,
            4.04854425681090213714335979133807e-04, // N = 113
            1.13460065721315947646907762447199e-03,
            1.93619770255745986958784143894263e-03,
            2.71300553415214622948736788998758e-03,
            3.46765413778949609449608892930428e-03,
            4.22783675301201256058192257114570e-03,
            4.99736923841801339990498220799964e-03,
            5.75927432452592001632662999099921e-03,
            6.50834972907541730452463113465456e-03,
            7.25443562482007853892129745077000e-03,
            8.00098358553998599551615455993669e-03,
            8.74009715423504883469174586707595e-03,
            9.46785986312446113666307923040222e-03,
            1.01891295077848678674037330438296e-02,
            1.09061472133281517349345790535153e-02,
            1.16141559009874974217613186056042e-02,
            1.23102595419394798825774017814183e-02,
            1.29972732953008585782272987785291e-02,
            1.36766618470586364536556445159476e-02,
            1.43451565061390069744096109616294e-02,
            1.50005340839299023542041666701152e-02,
            1.56445707763738471596237644689609e-02,
            1.62782409845618029897718059828549e-02,
            1.68991269319162043527349226224032e-02,
            1.75054728474512630298498550018849e-02,
            1.80984551625723404100209990019721e-02,
            1.86787272173665544472420663169032e-02,
            1.92444240978762934335399847896042e-02,
            1.97941378967653458520459253122681e-02,
            2.03286705267696418686362846983684e-02,
            2.08484582266852264131884453490784e-02,
            2.13520314275737234377405826535323e-02,
            2.18382580667711920230367184103670e-02,
            2.23076942432819877448757495130849e-02,
            2.27606260248175255866964761253257e-02,
            2.31958887755068718372619684942038e-02,
            2.36125814725028533580530876179182e-02,
            2.40110936936184966861151934836016e-02,
            2.43916059940075570511286429109532e-02,
            2.47532037580798502940382377346396e-02,
            2.50951885612041569739716351250536e-02,
            2.54178348386583062568089275146122e-02,
            2.57212479828857892849569566351420e-02,
            2.60047287870536041054503328950886e-02,
            2.62677633311022978856996701324533e-02,
            2.65105451385762025395820273843128e-02,
            2.67331249347123878212784120478318e-02,
            2.69349966860487517739120022497445e-02,
            2.71158197923241812976602460594222e-02,
            2.72757297141034554810445911243733e-02,
            2.74147356920586872386369492460290e-02,
            2.75325106364013652560096545585111e-02,
            2.76288810142683236015237469018757e-02,
            2.77039389105926646406086177876205e-02,
            2.77576593729842273361452242852465e-02,
            2.77898855555865076372157318473910e-02,
            2.78006086006585100001142762948803e-02,
            3.90915649315165525650578315364214e-04, // N = 115
            1.09544774581676494437654234559432e-03,
            1.86948539049794620198197137028728e-03,
            2.61967148259253414244174251734876e-03,
            3.34840082427376780488392782331175e-03,
            4.08253277469900009016834374619975e-03,
            4.82596873651658462428537532673545e-03,
            5.56219082883947085749198890880507e-03,
            6.28597801067373295608176064774852e-03,
            7.00702336924278416235845057258302e-03,
            7.72892041939083219298511906458771e-03,
            8.44386127736928074338784711017070e-03,
            9.14782010487214837513025855741944e-03,
            9.84573026897666604695391612267485e-03,
            1.05400574018447035912204867713626e-02,
            1.12259764623539801120521985922096e-02,
            1.19004038082574092882737204490695e-02,
            1.25663435418484556449492117735645e-02,
            1.32255501650315552414349795640192e-02,
            1.38745915850606981595261046891210e-02,
            1.45109917324911831537637141309460e-02,
            1.51367907712192228258940573937252e-02,
            1.57533075260849128595985746414954e-02,
            1.63578889332766930220230960912886e-02,
            1.69484676856983609849471861252823e-02,
            1.75265425278505852790811303520968e-02,
            1.80931604001294439598712671113390e-02,
            1.86461594592584288532233216528766e-02,
            1.91837641265290605174786975339885e-02,
            1.97071491606809721941484525586930e-02,
            2.02171915021548548319074711798748e-02,
            2.07120672203955427659316512745136e-02,
            2.11902203202165816120494667984531e-02,
            2.16526269985368481629794956688784e-02,
            2.21000614087627812731629006748335e-02,
            2.25309479997394326855619794969243e-02,
            2.29439034872242347828930064679298e-02,
            2.33397843304292730570725922234487e-02,
            2.37193087488832173026498395529416e-02,
            2.40810933295038838430901506626469e-02,
            2.44238953340682046766474400101288e-02,
            2.47485044866966839849364845349555e-02,
            2.50556173981367792669150418305435e-02,
            2.53440051086880717423621689476931e-02,
            2.56125419858145644824709563636134e-02,
            2.58619887037024528964046510282060e-02,
            2.60930465932716834642768333196727e-02,
            2.63046142212462509546444522356978e-02,
            2.64956647494280807253463905226454e-02,
            2.66669579323899515188589504077754e-02,
            2.68192209479638163371895132058853e-02,
            2.69514592602958652500788616634964e-02,
            2.70627293311034959610861250212110e-02,
            2.71538119767414480587586211868256e-02,
            2.72254780070373680889161960294587e-02,
            2.72768227061053053494887876695429e-02,
            2.73069715408828482539060900080585e-02,
            2.73167443997778501552087249137912e-02,
            3.77647427242911945272779705717880e-04, // N = 117
            1.05837011439779407270811439900626e-03,
            1.80617313800840234225275615642659e-03,
            2.53094782753637316530248568824391e-03,
            3.23517931884357472574476055626747e-03,
            3.94473943923181677440048531479988e-03,
            4.66323069988397020252390845485024e-03,
            5.37484887798359619454080515765781e-03,
            6.07477027746751094272603666013310e-03,
            6.77221488932363072099640532997000e-03,
            7.47044550924513568040952193882731e-03,
            8.16212453558611862602933939569994e-03,
            8.84362404397421794643996406648512e-03,
            9.51951620381025556683063371110620e-03,
            1.01919338946583164229320317417660e-02,
            1.08564635664575460244352100858123e-02,
            1.15104247450775829669789018794290e-02,
            1.21564828797915101821214278743355e-02,
            1.27960449741006798002329603036742e-02,
            1.34260808219927568057938671586271e-02,
            1.40445323370501588128300696212136e-02,
            1.46530936467704070436113283903978e-02,
            1.52527121337979968546116893435283e-02,
            1.58411455621914956659601614319399e-02,
            1.64167657806962852262699925631750e-02,
            1.69807046277164266911974266349716e-02,
            1.75336071893156322798468238488567e-02,
            1.80737404254324510177731610838237e-02,
            1.85997937732175072644835722712742e-02,
            1.91125463991515566475332121854080e-02,
            1.96124376931245229804812169049910e-02,
            2.00980961418281353636494657166622e-02,
            2.05684607808666840289557597998282e-02,
            2.10240778328049451872949759945186e-02,
            2.14652432242582701105160225552027e-02,
            2.18908619216992700318158426853188e-02,
            2.23000799702017249437346890772460e-02,
            2.26932844628910772299956732922510e-02,
            2.30706695193658786746659927757719e-02,
            2.34313646795689216328906212538641e-02,
            2.37746956782716109546349514403119e-02,
            2.41009384545167702762480388400945e-02,
            2.44102138598359594268139005635021e-02,
            2.47018430569586472378418307016545e-02,
            2.49753137873618136222120256206836e-02,
            2.52308230415292725212772495524405e-02,
            2.54684380204729630958748742841635e-02,
            2.56876501029307188761485747363622e-02,
            2.58880977463781351832761146170014e-02,
            2.60699208417950085980852037437216e-02,
            2.62331460610968833502276709168655e-02,
            2.63774210266963238247228673571954e-02,
            2.65025281123261423343873133262605e-02,
            2.66085646530480127158746483928553e-02,
            2.66955248192748822999575963876850e-02,
            2.67632035784580481208028146511424e-02,
            2.68115238229036725869924850940151e-02,
            2.68405493251363570783585288381801e-02,
            2.68502454488868912141352751632439e-02,
            3.65078057985456676855923197067000e-04, // N = 119
            1.02306558201893595290432603661657e-03,
            1.74601192536355661819036377835346e-03,
            2.44676829912422299367902311928447e-03,
            3.12761049197181773690035200274906e-03,
            3.81365291023223794766860983429524e-03,
            4.50856663104702657524081033102448e-03,
            5.19696383430109497963966802558389e-03,
            5.87400848501561014675109717586565e-03,
            6.54878027494493111099194138091661e-03,
            7.22466002612738838334349722458683e-03,
            7.89439419219833612983983073263516e-03,
            8.55426260451658260208773754129652e-03,
            9.20889637165119880057861934119501e-03,
            9.86061950098042830359368338122295e-03,
            1.05049632261270259325769416136609e-02,
            1.11390861716998430114289320158605e-02,
            1.17658136266726044000252571208875e-02,
            1.23868012490963921856668150667247e-02,
            1.29988794858331285775321362052637e-02,
            1.35997725844584586157859362742784e-02,
            1.41914008729523751645151818934210e-02,
            1.47750081640068645777441602717772e-02,
            1.53481501390926519667878835662123e-02,
            1.59089304494055353011994213829894e-02,
            1.64587583817501006966388388264022e-02,
            1.69986181370096987863771431648274e-02,
            1.75265213303943019618191812014629e-02,
            1.80408412909007845326136987296195e-02,
            1.85426786673440237296350829865332e-02,
            1.90328524838918738959492316098476e-02,
            1.95096867277235429261050825289203e-02,
            1.99717567379526297899339226660231e-02,
            2.04199710253188358721754269708981e-02,
            2.08550455126902747893247180854814e-02,
            2.12755326971375141598130653619592e-02,
            2.16801660166034658450140426566577e-02,
            2.20697348529071343814500494318054e-02,
            2.24448951052200230960043114691871e-02,
            2.28043751663471634671953580664194e-02,
            2.31470365748371667558025421840284e-02,
            2.34735985042059183691698365237244e-02,
            2.37846882120206076782764625932032e-02,
            2.40791748791160005460643134256316e-02,
            2.43560265009216472820163801316085e-02,
            2.46159266741874764583553059082988e-02,
            2.48594979119677421397494043731058e-02,
            2.50857253235578780969916579124401e-02,
            2.52936667517428825924241664324654e-02,
            2.54839959210502696451694504276020e-02,
            2.56573495857394459629396976652060e-02,
            2.58128100395869780614432897891675e-02,
            2.59495112888946943829893143629306e-02,
            2.60681371123701322023435977826011e-02,
            2.61693542620219689320837375134943e-02,
            2.62523270664075034086515358922043e-02,
            2.63162534981451375071248577341976e-02,
            2.63618435229457555302179372347382e-02,
            2.63898076154782078306393344746539e-02,
            2.63993789295778047421237033631769e-02,
            3.53093520084849172083196755522749e-04, // N = 121
            9.89571115950004659422845065819274e-04,
            1.68881658669494403093858103659386e-03,
            2.36661114697426979563976701115280e-03,
            3.02530527821434332483296891780356e-03,
            3.68912213435799605718012905697378e-03,
            4.36146638924708208995273395203185e-03,
            5.02758855697252836358668304228559e-03,
            5.68300310799131971895015169593535e-03,
            6.33636534216348076137270695085135e-03,
            6.99076245664267004881198275256793e-03,
            7.63935787810085704940821216268887e-03,
            8.27878115796717994889775127376197e-03,
            8.91334185215238335164844585278843e-03,
            9.54507013554981020853063000686234e-03,
            1.01698598486048459588193537683765e-02,
            1.07852228420445457601761773958060e-02,
            1.13936849294165726265148919083003e-02,
            1.19965963864798828147906206709195e-02,
            1.25911404187634759499481162947632e-02,
            1.31754066037134184158352567806105e-02,
            1.37510109230750358216832651692130e-02,
            1.43188721544276597458233979409670e-02,
            1.48769056234409682848429667956225e-02,
            1.54235980364135338155362475731636e-02,
            1.59600374493414562393489575242711e-02,
            1.64868578020029125930090430074415e-02,
            1.70024452957587488000079645189544e-02,
            1.75055780683059658553446524820174e-02,
            1.79970118283644883727667718176235e-02,
            1.84771856788641802848971451567195e-02,
            1.89448180410103153570311462772224e-02,
            1.93989142700467485924686883436152e-02,
            1.98400093852729338117502067007081e-02,
            2.02684056500298838410234480988947e-02,
            2.06830736179305745003897953893102e-02,
            2.10832054091250609140217875392409e-02,
            2.14691842165754959159684744918195e-02,
            2.18412143691306404047480782537605e-02,
            2.21984694712669961003115304265521e-02,
            2.25403022380505843602627180644049e-02,
            2.28669888878399764353677170447554e-02,
            2.31786626241193595421297146685902e-02,
            2.34746687593110382741290464991835e-02,
            2.37545034365186959190996418556097e-02,
            2.40183661731710323961053177299618e-02,
            2.42663377114907714837688246234393e-02,
            2.44979145258998713685638648485110e-02,
            2.47127249670960509597694709782445e-02,
            2.49109126326128756112598949812309e-02,
            2.50925186266442515337082852511230e-02,
            2.52571769735132345413575194470468e-02,
            2.54046411432650130757249229418449e-02,
            2.55350129860712551921331225912581e-02,
            2.56483023113076545607125211745370e-02,
            2.57442717748336546979004424429149e-02,
            2.58227959361498476953400427191809e-02,
            2.58839441460039648701396686192311e-02,
            2.59276995637101499714294305931617e-02,
            2.59539479341057872929798833183668e-02,
            2.59626833396368744688587071323127e-02,
            3.41719892175625409528466613906517e-04, // N = 123
            9.57626730429707436961783706408369e-04,
            1.63437621843620000186558804955439e-03,
            2.29042751022067456526110085235359e-03,
            2.92794402925707292553725302752810e-03,
            3.57045900608622679417436529547558e-03,
            4.22143197723970613893795800208864e-03,
            4.86649212256053034092451170522509e-03,
            5.50114666466848274001266716481950e-03,
            6.13391752819161719528784360022655e-03,
            6.76799034872303459375864065350470e-03,
            7.39660819010769330500432161557001e-03,
            8.01632254467577257117660849417007e-03,
            8.63148856579408138567366393090197e-03,
            9.24429987508506439963795742187358e-03,
            9.85060548725638640554791436443338e-03,
            1.04477786229770375908687540800202e-02,
            1.10384808647819611382434601409841e-02,
            1.16242768474777678766596267223576e-02,
            1.22022304064804774231811634876976e-02,
            1.27702428201099289772901812511918e-02,
            1.33301247978780106756557799485563e-02,
            1.38830514927025371746394100114230e-02,
            1.44267637885174306033864155551782e-02,
            1.49595162675938489482696525101346e-02,
            1.54826369491387720589425924799798e-02,
            1.59970534152014641493533275706795e-02,
            1.65009311034759117986503440533852e-02,
            1.69927748385710758460831470983976e-02,
            1.74736188761436261884796294907574e-02,
            1.79442310499626847541954077769333e-02,
            1.84030666484911176183913994464092e-02,
            1.88488171465532317050417532300344e-02,
            1.92823315728945857139287056725152e-02,
            1.97042755610167021063094949795413e-02,
            2.01133155331176156910277796896480e-02,
            2.05082883737674748214629971698741e-02,
            2.08899257342916866431181688312790e-02,
            2.12588308265912254158003236170771e-02,
            2.16138318553032206248420976635316e-02,
            2.19538830286163805238786039808474e-02,
            2.22796439427585084291916217580365e-02,
            2.25916842253013720742682579611937e-02,
            2.28889610296301240777161467576661e-02,
            2.31705257730093587553721334870716e-02,
            2.34369979580673973296178758118913e-02,
            2.36889354512221893267476247046943e-02,
            2.39254012621366307644876769700204e-02,
            2.41455287920958570901941442343741e-02,
            2.43499210573638602550516907285783e-02,
            2.45391413584526985047773450787645e-02,
            2.47123413642655505306766627882098e-02,
            2.48687241848650139597332042740163e-02,
            2.50088945299346658568406809308726e-02,
            2.51334352407285716024532007395464e-02,
            2.52415730131379974221506046205832e-02,
            2.53325700400168808690271049499643e-02,
            2.54070473028063167908463526600826e-02,
            2.54656192691375404812959004630102e-02,
            2.55075760862055710143092568387146e-02,
            2.55322291096868950188714109117427e-02,
            2.55402277932229235246630594247108e-02
        };

        #endregion
    }; // class math
}